Systems Lab
Dept. Of ECE, SJCET, Palai 1
DATE: 08-02-2011
EXPERIMENT NO.1
FAMILIARISATION OF MATLAB
AIM
To familiarize with MATLAB and its functions.
THEORY
MATLAB is an ideal software tool for studying digital signal processing. The plotting capacity
of MATLAB makes it possible to view the result of processing and gain understanding into
complicated operations. The tool box support a wide range of signal processing from waveform
generation to filter design and implementation, parametric modelling and spectral analysis. There are
two categories of tools Signal processing functions Graphical interaction tools. The first category of
tools is made of functions that we can call from the common line or from your own application. Many
of the functions are MATLAB statements that implement specialized signal processing algorithm.
(a) DEFINTION OF VARIABLES
Variables are assigned numerical values by typing the expression directly
Eg: a=1+2 yields a=3
The answer will not be displayed when semicolon is put at the end of an expression
Eg: a=1+2
MATLAB utilizes the following arithmetic operations
+ Addition
- Subtraction
* Multiplication
/ Division
ˆpower operation
„Transpose
A variable can be assigned using a formula that utilizes these operations and either numbers or
previously defined variables.
Eg: since „a‟ was defined previously the following expression is valid, B=z*a.To determine the value
of a previously defined quantity type the quantity by b=6. If your expression does not fill on the line,
use an ellipse and continue on the next line.
C=1+2+3+. . . . . . . . . . . . ..+5+6+7. These are certain predefined variables which can be used at any
time, in the same manner as user defined variables.
i=sqrt(-1); j=sqrt(-1)
Systems Lab
Dept. Of ECE, SJCET, Palai 2
pi=3.1416
Eg: y=2*(1+4*j)yields y=2.000+8.000y
These are also a number of predefined functions that can be used when defining a variable.
Some common functions that are used in this text are Abs- magnitude of a number Angle- angle of a
complex numberCos- cosine function, assume arguments in radian.
Exp-exponential functions
For example with y defined as aboveE= abs(y), yields e=8.2462, c=angle(y) yields c=1.3258
with a=3 as defined previously c=cos(a)yields, c= -0.9900c = exp(a), yields c=20.0855.Note that exp
can be used on complex numbers example with y = 2 + 8i as defined above
c = -1.0751 + 7.3104i which can be verified by using Euler‟s formula
c = c2cos(8) + jc2sin(8).
(b) DEFINTION OF MATRICES
MATLAB is based on matrix and vector algebra. Even scalars are treated 1x1 matrix.
Therefore, vector and matrix operation are simple as common calculator operations. Vectors can be
defined in two ways. The first method is used for arbitrary elements, v=[1 3 5 7] creates 1x4 vector
elements with elements 1 3 5 &7. Note that commas would have been used in the place of spaces to
separate the elements. Additional elements can be added to the vector v(5)=8 yields the vector v =
[1357]. Previously defined vectors can be used to define a new vectors. For example with we defined
above a= [910]; b = [v a]; creates the vector b = [1357910]. The second method is used for creating
vector with equally spaced elements t=0:0.1:10; creates 1x101 vector with elements0,0.1,0.2. . . . . 10.
Note that the middle number defines the increments is set to a default of 1k=0,10 creates 1x11 vector
with the elements 0,1,2. . . .10. Matrices are defined by entering the element row by row. M = [124;
368] creates the matrix M= 1 2 43 6 8 There are number of special matrices that can be defined Null
matrix: [ ];
Nxm matrixes of zero: M=zeros (m,m);
Nxm matrix of ones: M= ones (n,m);
Nxn matrix of identity: M=eye (n)
A particular elements of matrix can e assigned M(1,2)=5 place the number 5 in the first
row,2nd column. Operations and functions that were defined for scalars in the previous section can be
used on vectors and matrices. For example a=[1 2 3]; b=[4 5 6]; c=a+b yield c=579. Functions are
applied element by element. For example t=0:„0; x=cos(2*t) creates a vector „x‟ with elements equal
to cos(2t) for t=0,1,2. . . ..10
(c) GENERAL INFORMATION
MATLAB is case sensitive. So „a‟ and „A‟ are two different names. Comment statements are
preceded by a %.
Systems Lab
Dept. Of ECE, SJCET, Palai 3
1) M-files M-files are macros of MATLAB commands that are stored as ordinary text file
with the extension „in‟ that is „filename.m‟. An m-file can be either a function with input and output
variables or a set of commands. MATLAB requires that the m-file must be stored either in the
working directory or in a directory that is specified in the MATLAB path list. The following
commands typed from within MATLAB demonstrate how this m-file is used. X=2,y=3,z=y plusx(y,x)
MATLAB m-files are most efficient when written in a way that utilizes matrix or vector operations,
loops and if statements are available, but should be used sparingly since they are computationally
inefficient. An examples is For k=1:10 x(k)=cos(k) end; This creates a 1x10vector „x‟ containing the
cosine of the positive integers from 1 to 10. This operation is performed more efficiently with the
commands k=1:10 x=cos(k) which utilizes a function of a vector instead of a for loop. An if statement
can be used to define combinational statement.
(d) REPRESENTATION OF SIGNALS
A signal can be defined as function that conveys information, generally about or behaviour of
physical system; signals are represented mathematically as functions of one or more independent
variables. The independent variables is the mathematical expression of a signal may be either
continuous is discrete. Continuous time signals are defined along a number of times and thus they
are represented by a continuous independent variable. TheMATLAB is case sensitive. Discrete time
signals are represented mathematically.Continuoustimesignals are often referred to as analog
signals. Discrete time signals are defined at discrete times and thus the independent variable has
discrete values. In a sequence of numbers x, the nthnumber in the sequence is denoted as x[n]. The
basic signals used in digital signal processing are the unit impulse signal [U+0260](n), exponential of
the form au[n], sine waves and their generalization to complex exponentials. Since the only numerical
data type in MATLAB is the m x nmatrix, signals must be represented as vectors either mx1 matrix if
column vector 1xn matrices if row vectors. A constant will be treated as 1x1 matrix. The signals are
sampling frequency Fs,which is greater than twice the maximum frequency of the signal. In time
domain, the signals are represented as time versus amplitude. In MATLAB you can generate time
base for given signals T=t start: 1/Fs:t-stop,tstart is the starting time of the signal t-sto is the stop time
of the signal and Fs sampling frequency. 1/Fs is the time period between the two samples. In signals
like speech if the data secured length is too long, plotting of the whole signal will not be clean view.
In that case we can use step function.
RESULT
The familiarization of MATLAB was completed.
Systems Lab
Dept. Of ECE, SJCET, Palai 4
DATE: 08-02-2011
EXPERIMENT NO: 2
BASIC DISCRETE TIME SIGNALS
AIM
To plot the following waveforms
1. Step Function
2. Impulse Function
3. Exponential Function
4. Ramp Function
5. Sine Function
THEORY
A digital signal can be either deterministic signal that can be predicted with certainty or
random signal that is unpredictable. Due to ease in signal generation and need for predictability,
deterministic signal can be used for system simulation studies.Standard forms of some deterministic
signal that is frequently used in DSP are discussed below:
1. Impulse:the simplest signal is the unit impulse signal which is defined as
δ (n) = 1 for n = 0
= 0 for n ≠ 0
2. Step:the general form of step function is
u (n) = 1 for n ≥ 0
= 0 for n< 0
3. Exponential:the decaying exponential is a basic signal in DSP.Their general form is given by
x (n) = a n for all n.
4. Ramp:signal is given by
ur (n) = n for n ≥ 0
= 0 for n < 0
5. Sine:A sinusoidal sequence is defined as x(n) = sin(n).
ALGORITHM
1. Start
2. Generate the time axis
3. Define A as sine function
4. Plot the sine wave
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Dept. Of ECE, SJCET, Palai 5
5. Define B as exponential signal
6. Plot the exponential signal
7. Define r(n) as ramp signal
8. Plot the ramp signal
9. Define unit impulse signal
10. Plot the signal
11. Define unit step signal
12. Plot the signal
13.Stop
MATLAB FUNCTIONS USED
• CLC: clc clears all input and output from the Command Window display, giving you a ”clean
screen. “After using clc, you cannot use the scroll bar to see the history of functions, but you still can
use the up arrow to recall statements from the command history.
• CLEAR ALL: clear removes all variables from the workspace. This frees up system memory.
• CLOSE ALL: Closes all the open figure windows
• SUBPLOT: subplot divides the current figure into rectangular panes that are numberedrowwise.
Each pane contains an axes object. Subsequent plots are output to the current pane.
• STEM: A two-dimensional stem plot displays data as lines extending from a baseline along the x-
axis. A circle (the default) or other marker whose y-position represents the data value terminates each
stem.
• TITLE: Each axes graphics object can have one title. The title is located at the top and in the centre
of the axes.
• XLABEL: Each axes graphics object can have one label for the x-, y-, and z-axis. The label appears
beneath its respective axis in a two-dimensional plot and to the side or beneath the axis in a three-
dimensional plot.
• YLABEL: Each axes graphics object can have one label for the x-, y-, and z-axis. The label appears
beneath its respective axis in a two-dimensional plot and to the side or beneath the axis in a three-
dimensional plot.
• ZEROS: Create array of all zeros
• ONES: Create array of all ones
• SIN: The sin function operates element-wise on arrays. The function‟s domains and ranges include
complex values. All angles are in radians.
• EXP: The exp function is an elementary function that operates element-wise on arrays. Its domain
includes complex numbers.
Systems Lab
Dept. Of ECE, SJCET, Palai 6
PROGRAM
%Generation of Basic Discrete Signals
clear all
clc
close all
%Generation of Sinusoidal signal
n =0:0.5:10;
y=sin(n);
subplot(3,2,1);
stem(n,y);
xlabel(' Samples ');
ylabel(' Amplitude');
title (' Sine');
%Generation of Exponential signal
y=exp(n);
subplot(3,2,2);
stem(n,y);
xlabel (' Samples ');
ylabel(' Amplitude');
title (' Exponential');
%Generation of Ramp signal
n =1:10;
y=n;
subplot(3,2,3);
stem(n,y);
xlabel (' Samples ');
ylabel(' Amplitude');
title (' Ramp');
%Generation of Unit Impulse signal
n =-10:10;
y=[zeros(1,10) 1 zeros(1,10)];
subplot(3,2,4);
stem(n,y);
xlabel (' Samples ');
ylabel (' Amplitude');
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Dept. Of ECE, SJCET, Palai 7
title(' Impulse');
%Generation of Unit Step signal
n =-10:10;
y=[zeros(1,10) 1 ones(1,10)];
subplot(3,2,5);
stem(n,y);
xlabel (' Samples ');
ylabel(' Amplitude');
title (' Step');
OUTPUT
RESULT The MATLAB program to generate basic discrete signals is executed and output
waveforms are obtained.
Systems Lab
Dept. Of ECE, SJCET, Palai 8
DATE: 17-02-2011
EXPERIMENT NO: 3
IMPULSE RESPONSE & STEP RESPONSE
AIM
Write a MATLAB program to find the impulse response and step response of the system given
by y(n) = x(n) + x(n-1) – 0.7y(n-1) at -20 ≤ n ≤ 100.
THEORY
The impulse response of a given system is its response to impulse function input. We know
that y[n]=impulse response h[n],when input x[n] is unit impulse function Step response of a system is
its output for step function.
ALGORITHM
1. Start
2. Input the coefficients of x(n).
3. Generate impulse signal.
4. Input the coefficients of y(n).
5. Obtain the impulse response using filter function
6. Plot the impulse response.
7. Generate step signal.
8. Obtain the step response using filter function.
9. Plot the step response.
10. Stop.
MATLAB FUNCTIONS USED
FILTER: One dimensional digital filter. Y=FILTER (B, A, X) filter the data in vector X with the filter
described by vectors A and B to create the filtered data Y. The filter is a “Direct Form II Transposed”
implementation of the standard difference equation: a(1) * y(n) = b(1) * x(n) +b(2) * x(n - 1) + .... +
b(nb + 1) * x(n - nb) - a(2) * y(n - 1) - . . . a(na + 1) * y(n - na) If a(1) is not equal to 1, filter
normalizes the filter coefficients by a(1).
Systems Lab
Dept. Of ECE, SJCET, Palai 9
PROGRAM
clc
clear all
close all
x = [ 1 1];
y = [1 0.7];
n = -20:1:10;
imp = [zeros(1,20) 1 zeros(1,10)];
h = filter (x, y, imp);
subplot (2, 1, 1);
stem (n,h);
title(' Impulse Response ');
xlabel (' Samples ');
ylabel (' Amplitude ');
stp = [zeros(1,10 1 ones(1,20)];
h = filter(x,y,stp);
subplot ( 2, 1, 2);
stem(n,h);
title (' Step Response ');
xlabel (' Samples ');
ylabel (' Amplitude ');
Systems Lab
Dept. Of ECE, SJCET, Palai 10
OUTPUT
RESULT
The MATLAB program to find the impulse response and step response of the given system is
executed and output waveform is obtained.
Systems Lab
Dept. Of ECE, SJCET, Palai 11
DATE: 24-02-2011
EXPERIMENT NO: 4
LINEARITY, STABILITY & CAUSALITY
AIM
Write a MATLAB program to find whether the given systems are linear, stable and causal.
1. y(n) = x(n) – 0.9y(n-1)
2. y(n) = exp x(n)
THEORY
A system is linear if and only if T [a1x1[n] + a2x2n]] = a1T [x1[n]] + a2T [x2[n]], for any
arbitrary constants a1 and a2.
Let x[n] be bounded input sequence and h[n] be impulse response of the system and y[n], the
output sequence. Necessary and sufficient boundary condition for stability is8n = -8|h[n]| < 8.
Causal system is a system where the output depends on past or current inputs but not on the
future inputs. The necessary condition is h[n] = 0; < 0, where h[n] is the impulse response.
ALGORITHM
1. Start
2. Input the coefficients of x(n) and y(n)
3. Generate random signals x1 and x2.
4. Check for linearity using filter function of the given system and display
5. Generate impulse signal.
6. Check for causality using filter function of the given system and display
7. Obtain the absolute value of impulse response and check for the stability of the system and display.
8. Stop
MATLAB FUNCTIONS USED
• RAND: Uniformly distributed pseudo random numbers. R=RAND (N) returns an N-by-N matrix
containing pseudo-random values drawn from a uniform distribution on the unit interval. RAND (M ,
N)or RAND([M, N]) returns an M-by-N matrix.
Systems Lab
Dept. Of ECE, SJCET, Palai 12
• DISP: Display array. DISP(X) displays the array, without printing the array name. In all other ways
it‟s the same as leaving the semicolon of an expression except that empty arrays don‟t display.
• ABS: Absolute value. ABS(X) is the absolute value of the elements of X.
• SUM: Sum of elements. S=SUM(X) is the sum of the elements of the vector X.
PROGRAM
%Program to find linearity of system 1
clc
clear all
close all
% System 1
% Linearity
b = [1 0];
a = [1 0.9];
x1 = rand (1,10);
x2 = rand (1,10);
y2 = filter (b, a, 2.*x1);
y5 = filter (b, a,2.* x2);
y = filter (b, a, x1);
y0 = filter (b, a, x2);
y6 = y2+y5;
y7 = y+y0;
if (y6-y7 ~= 0)
disp (' Linear ')
else
disp (' Non Linear ')
end;
% Causality--------%%%
n= -10:1:10;
x = [zeros(1,10) 1 zeros(1,10)];
y1 = filter (a, b, x);
Systems Lab
Dept. Of ECE, SJCET, Palai 13
subplot (2, 1, 1);
stem (n1,y1);
xlabel (' Samples ');
ylabel (' Amplitude ');
% Stability
T = abs (y1);
t = sum (T);
if (t < 1000)
disp (' Stable ')
else
disp (' Unstable ')
end;
%%%%%%%%%% % System 2%%%%%%%%%%%%%%%%%%%%%
% 1 % Linearity
y8 = exp (x2);
y9 = exp ( x3);
y10 = 5*y8+5*y9;
y11 = exp(5*x2+5*x3);
if (y11-y10~=0)
disp (' 2Linear ')
else
disp (' 2Non Linear ')
end;
% 2 % Causality
Y8= exp (x);
subplot (2, 1, 2);
stem (n1,y8);
xlabel (' Samples ');
ylabel (' Amplitude ');
Systems Lab
Dept. Of ECE, SJCET, Palai 14
% 3 % Stability
T1= abs (y8);
t1 = sum (T1);
if (t1 < 1000)
disp (' 2Stable ')
else
disp (' 2Unstable ')
end;
OUTPUT
System 1
Linear.
Stable.
System 2
Non Linear.
Stable.
Systems Lab
Dept. Of ECE, SJCET, Palai 15
RESULT
The MATLAB program to find the linearity, causality, and stability of 2 systems given is
executed and output is obtained
System 1
System 2
Linear Non Linear
Stable Stable
Causal Non Causal
Systems Lab
Dept. Of ECE, SJCET, Palai 16
DATE: 15-03-2011
EXPERIMENT NO: 5
CONVOLUTION
AIM
Write a MATLAB program to obtain linear and circular convolution of the following sequences
1. x(n) = [1 2 3 4]
h(n) = [1 2 3]
2. x(n) = u(n)
h(n) = u(n-2)
THEORY
Convolution is used to find the output response of a digital system. The linear convolution of
two continuous time signals x[n] and h[n] is defined by y[n] = x[n] * h[n].
Circular Convolution of two sequences x1[n] and x2[n], each of length N is given by y[n] = If
the length of sequence is not equal, zero padding is done. Convolution operation will result in the
convolved signal be zero outside of the range n= 0,1,...,N-1.
ALGORITHM
1. Start
2. Input the sequences
3. Input the length of sequences
4. Calculate the linear convolution.
5. Calculate the circular convolution.
6. Stop
MATLAB FUNCTIONS USED
• CONV: Convolution and polynomial multiplication. C = CONV (A,B) convolves vectors A and B.
The resulting vector is length LENGTH(A) + LENGTH(B) – 1 .If A and Bare vectors of polynomial
coefficients, convolving them is equivalent to multiplying the two polynomials.
• LENGTH: Length of vector. LENGTH(X) returns the length of vector X.
Systems Lab
Dept. Of ECE, SJCET, Palai 17
• CCONV: Convolution and polynomial multiplication. C = CONV (A,B) convolves vectors A and B.
The resulting vector is length LENGTH(A) + LENGTH(B) – 1 .If A and Bare vectors of polynomial
coefficients, convolving them is equivalent to multiplying the two polynomials.
PROGRAM
%program to find convolution of two sequences
clc
close all
clear all
n = -10:10;
x1 = [1 2 3 4];
subplot(4,2,1);
stem(x1);
title('-----x1(n)----');
h1 = [1,2,3];
subplot(4,2,3);
stem(h1);
title('-----h1(n)----');
%%%%%linear convolution%%%%%%
l1 = conv(x1,h1)
subplot(4,2,5);
stem(l1);
title('-----linear convolution-1--');
%%%%%%%%%% circular convolution %%%%%%%%%%%5
x1 = [1 2 3 4];
h1 = [1 2 3 0];
c1 = cconv(x1,h1,4)
Systems Lab
Dept. Of ECE, SJCET, Palai 18
subplot(4,2,7);
stem(c1);
title('-----circular convolution-1---');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
x2 = [zeros(1,10) ones(1,11)];
subplot(4,2,2);
stem(n,x2);
title('-----x2(n)----');
h2 = [zeros(1,12) ones(1,9)];
subplot(4,2,4);
stem(n,h2);
title('-----h2(n)----');
%%%%%linear convolution%%%%%%
l2= conv(x2,h2)
subplot(4,2,6);
stem(l2);
title('-----linear convolution--2--');
%%%%%%%%%% circular convolution %%%%%%%%%%%
c2 = cconv(x2,h2,8)
subplot(4,2,8);
stem(c2);
title('-----circular convolution--2----');
Systems Lab
Dept. Of ECE, SJCET, Palai 19
OUTPUT
RESULT
The MATLAB program to find the linear convolution and circular convolution of given
sequences is executed and output is obtained.
Systems Lab
Dept. Of ECE, SJCET, Palai 20
DATE: 15-03-2011
EXPERIMENT NO: 6
CONVOLUTION USING DFT
AIM
1. Write a MATLAB program to obtain linear convolution of
x(n) = [1 2 3 4]
h(n) = [1 2 2 -1] using DFT.
2. Write a MATLAB program to obtain circular convolution of
x(n) = u(n), h(n) = u(n-3)
THEORY
Convolution is used to find the output response of a digital system. The linear convolution of
two continuous time signals x[n] and h[n] is defined by y[n] = x[n] * h[n] = Let X(k) and H(k) be the
Fourier transforms of x[n] and h[n] respectively. Then by DFT method, convolution of x[n] and h[n]
is given by: x[n]*h[n]= Inverse Fourier transform of X(k).H(k).
Circular convolution of two sequences x1[n] and x2[n], each of length N is given by y[n] = If
the length of sequence is not equal, zero padding is done. Convolution operation will result in the
convolved signal be zero outside of the range n= 0,1,...,N-1.Then by DFT method, convolution of x[n]
and h[n] is given by: x[n]*h[n]= Inverse Fourier transform of X(k).H(k).
ALGORITHM
1. Start
2. Input the sequences
3. Input the length of the sequences.
4. Find the FFT of the sequences
5. Multiply the FFT of the sequences.
6. Calculate the IFFT
7. Stop
Systems Lab
Dept. Of ECE, SJCET, Palai 21
MATLAB FUNCTIONS USED
• FFT: Discrete Fourier Transform. FFT(X) is the discrete Fourier transform(DFT) of vectorX.
FFT(X,N) is the N-point FFT, padded with zeros if X has less than N points and truncated if it has
more.
• IFFT: Inverse discrete Fourier transform. IFFT(X) is the inverse discrete Fourier transform of X.
IIF(X,N) is the N-point inverse transform.
PROGRAM
clc; close all; clear all;
x1 = [1 2 3 4];
subplot(4,2,1);
stem(x1);
title('-----x1(n)----');
h1 = [1 2 2 -1];
subplot(4,2,3);
stem(h1);
title('-----h1(n)----');
l = conv(x1,h1)
subplot(4,2,5);
stem(l);
title('-----linear convolution----')
dx1 = fft(x1,7);
dh1 = fft(h1,7);
dl = dx1.*dh1;
k1 = ifft(dl)
subplot(4,2,7);
stem(k1);
Systems Lab
Dept. Of ECE, SJCET, Palai 22
title('-----linear convolution--dft--');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x2 = ones(1,6);
subplot(4,2,2);
stem(x2);
title('-----x2(n)----');
h2 = [zeros(1,3) ones(1,3)];
subplot(4,2,4);
stem(h2);
title('-----h2(n)----');
c = cconv(x2,h2,6)
subplot(4,2,6);
stem(c);
title('-----circular convolution------');
dx2 = fft(x2,6);
dh2 = fft(h2,6);
dc = dx2.*dh2;
k2 = ifft(dc)
subplot(4,2,8);
stem(k2);
title('-----circular convolution--dft----');
Systems Lab
Dept. Of ECE, SJCET, Palai 23
OUTPUT
RESULT
The MATLAB program to find linear convolution and circular convolution of given
sequences using DFT is executed and output is obtained.
Systems Lab
Dept. Of ECE, SJCET, Palai 24
DATE: 22-03-2011
EXPERIMENT NO: 7
CORRELATION
AIM
a) Write a MATLAB program to compute autocorrelation of sequence x(n) = 0.9 n , n= 0 to 20 and
verify the property.
b) Compute cross-correlation of sequences x(n) = {1,2,3,4,5,6} and y(n) = x(n-3) and verify the
property.
THEORY
Autocorrelation is the cross-correlation of a signal with itself. The autocorrelation sequence of
x(n) is given by
RXX[l] = ∑ ( ) ( )
Cross correlation is a measure of similarity of two signals, commonly used to find features in
an unknown signal by comparing it to a known one. The correlation sequence of x(n) and y(n) is
given by
RXY[l] = ∑ ( ) ( ) l=0,±1,±2,…
ALGORITHM
1. Start
2. Input the sequences
3. Find the autocorrelation of the sequence
4. Check for the symmetry property of the sequence
5. Find the cross correlation of the sequences
6. Check for the symmetry property of the sequence
7. Stop
Systems Lab
Dept. Of ECE, SJCET, Palai 25
MATLAB FUNCTIONS USED
XCORR(A): when A is a vector, is the auto-correlation sequence.XCORR(A), when A is an M-by-N
matrix, is a large matrix with2*M-1 rows whose N^2 columns contain the cross-correlation sequences
for all combinations of the columns of A.
XCORR(A,B): where A and B are length M vectors (M>1), returns the length 2*M-1 cross-
correlation sequence C. If A and B are of different length, the shortest one is zero-padded.
FLIPLR: Flip matrix in left/right direction. FLIPLR(X) returns X with row preserved and columns
flipped in the left/right direction.
PROGRAM
clc;
clear all;
close all;
%autocorrelation of x(n)
n=0:20;
x=0.9.^n; % input sequence
y =xcorr(x); % autocorrelation
subplot(2,2,1);
stem (y);
xlabel (' Samples ')
ylabel ('Amplitude');
title(' Autocorrelation of x(n)');
%autocorrelation ofx(-n)
z =fliplr (y); % flip the matrix y
subplot(2,2,2);
stem (z);
xlabel (' Samples ');
ylabel(' Amplitude');
title (' Autocorrelation of x(-n)');
%cross correlation of x(n) & y(n)
x1= [1 2 3 4 5 6 0 0 0]; %input
h1 = [0 0 0 1 2 3 4 5 6]; % input
y1 =xcorr (x1, h1); % cross correlation of e and f
subplot(2,2,3);
stem (y1);
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xlabel (' Samples ') ;ylabel(' Amplitude');
title(' Cross correlation of x(n) and y(n)');
%cross correlation property
z1= fliplr (y1);
subplot(2,2,4); stem (z1);
xlabel (' Samples '); ylabel(' Amplitude');
title (' Cross correlation of x(-n) and h(-n)');
OUTPUT
RESULT
The MATLAB program to compute autocorrelation and cross correlation of the given
sequences is executed and output is obtained.
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Dept. Of ECE, SJCET, Palai 27
DATE: 22-03-2011
EXPERIMENT NO: 8
SAMPLING THEOREM
AIM
Write a MATLAB program to generate x(n) = sin 0.5πn for n to 50. Verify sampling theorem.
THEORY
Sampling Theorem: A band limited signal can be reconstructed exactly if it is sampled at a
rate at least twice the maximum frequency component in it.” Figure 1 shows a signal g(t) that is band
limited.
Figure 1: Spectrum of band limited signal g(t)
The maximum frequency component of g(t) is fm. To recover the signal g(t) exactly from its
samples it has to be sampled at a rate fs=2fm. The minimum required sampling rate fs = 2fm iscalled
Nyquist rate.
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ALGORITHM
1. Start
2. Generate the sine wave
3. Resample the signal at various values.
4. Obtain the output waveforms
5. Stop
MATLAB FUNCTIONS USED
RESAMPLE : Change the sampling rate of a signal.
Y = RESAMPLE(X,P,Q) resamples the sequence in vector X at P/Q times the original sample rate
using a polyphase implementation. Y is P/Q times the length of X (or the ceiling of this if P/Q is not
an integer). P and Q must be positive integers.
PROGRAM
% Verification of sampling theorem
clc;
clear all;
close all;
n = 0:0.5:50;
x = sin(0.5*pi*n);
subplot(4,1,1);
stem(x);
title('original');
y = resample(x,2,1);
subplot(4,1,2);
stem(y);
title('fs = 2fm');
y = resample(x,4,1);
subplot(4,1,3);
stem(y);
title('fs > 2fm');
y = resample(x,1,2);
subplot(4,1,4);
stem(y);
title('fs<2fm');
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OUTPUT
RESULT
The MATLAB program to generate sine wave and to verify sampling theorem is executed
and output is obtained.
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Dept. Of ECE, SJCET, Palai 30
DATE: 22-03-2011
EXPERIMENT NO: 9
POLE-ZERO PLOT
AIM
Write a MATLAB program to find poles and zeros of the system given by
y(n) = x(n) + 2x(n-1) – 0.9y(n-1)
THEORY
In mathematics, signal processing and control theory, a pole–zero plot is a graphical
representation of a rational transfer function in the complex plane which helps to convey certain
properties of the system such as:
Stability
Causal system / anticausal system
Region of convergence (ROC)
Minimum phase / non minimum phase
In general, a rational transfer function for a discrete LTI system has the form:
Where
zi such that P(zi) = 0 are the zeros of the system
zj such that Q(zj) = 0 are the poles of the system
In the plot, the poles of the system are indicated by an x while the zeroes are indicated by an o.
ALGORITHM
1. Start
2. Input the coefficients of the system
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3. Plot the zeros and poles of the system
4. Stop
MATLAB FUNCTIONS USED
ZPLANE: Z-plane zero-pole plot. ZPLANE (Z,P) plots the zeros Z and poles P (in column vectors)
with the unit circle for reference. Each zero is represented with a 'o' and each pole with a 'x' on the
plot. Multiple zeros and poles are indicated by the multiplicity number shown to the upper right of
the zero or pole.
PROGRAM
clc ;close all;clear all;
b = [1 2]; % coefficient of x
a = [1 0.9]; % coefficient of y
zplane (b, a);
OUTPUT
RESULT
The MATLAB program to find the poles and zeros of given system was executed and
output obtained correctly.
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Dept. Of ECE, SJCET, Palai 32
DATE: 22-03-2011
EXPERIMENT NO: 10
FIR FILTER DESIGN
AIM
1. Write a MATLAB program to design FIR filter and to plot magnitude and phase response for the
given specification using Kaiser window.
a. Pass band Ripple = 0.087 dB
b. Stop band attenuation = 60 dB
c. Pass band edge frequency = 0.4π
d. Stop band edge frequency = 0.6π
2. Design FIR filter using rectangular, hamming and hanning window
a. Pass band Ripple = 0.4 dB
b. Stop band attenuation = 44 dB
c. Pass band edge frequency = 3000Hz
d. Stop band edge frequency = 2000Hz
e. Sampling Frequency = 8000 Hz
THEORY
The basic idea behind the window design is to choose a proper ideal frequency selective filter
(which always has a non-causal, infinite duration impulse response), and then truncate ( or window)
its impulse response to obtain a linear phase and causal FIR filter. One possible way of obtaining FIR
filter is to truncate the Fourier series at n= ±( )
, where N is the length of the desired sequence but
abrupt truncation of the Fourier series results in oscillation in the pass band and stop band. These
oscillations are due to slow convergence of the Fourier series and this effect is known as Gibbs
phenomenon. To reduce this oscillations the Fourier coefficients of the filter are modified by
multiplying the infinite impulse response with a finite weighing sequence w(n) called a window.
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Rectangular window is given by
Wr (n) = 1; for n=±( )
= 0; otherwise
Frequency response: H( )
∫ (
) (
( ))
The convolution of the desired response and the rectangular window response gives rise to
ripples in both passband and stop band. This Gibbs phenomenon can be reduced by using a less abrupt
truncation of filter coefficients. This can be achieved using a window function that tapers smoothly
towards zero at both ends.
Hamming window is given by,
Wh(n) = 0.54+0.046cos(2πn/N-1); for n=±( )
= 0; otherwise
Frequency response: H( )
∫ (
) ( ( ))
This window generates less oscillation in the side lobes than the hamming window. At higher
frequencies the stop band attenuation is low when compared to the hanning window.
Hanning window is given by,
WHn(n) = .5+.5cos(2πn/N-1);for n=±( )
= 0; otherwise
This window results in smaller ripples in both passband and stop band of the filter. At higher
frequencies the stop band attenuation is even greater.
Kaiser window is given by,
WK(n) = ( (
( ))
( ) ; for n=±
( )
= 0; otherwise
This is one of the most useful and optimum window. It provides large main lobe width for the
given stop band attenuation, which implies the sharpest transition width. Α is the parameter that
depends on N (window length) and that can be chosen to yield the various transmission widths and
near optimum stop band attenuation.
ALGORITHM
1. Start
2. Input the design parameters of the system.
3. Find the order of the
4. Design the FIR filter using Kaiser Window
5. Plot the magnitude and phase response.
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6. Design the FIR filter using Hanning window
7. Plot the magnitude and phase response
8. Design the FIR filter using Hamming window
9. Plot the magnitude and phase response.
10. Design the FIR filter using Rectangular window
11. Plot the magnitude and phase response.
12. Stop
MATLAB FUNCTIONS USED
FIR1: FIR filters design using the window method. B = FIR1(N,Wn) designs an N'th order
low pass FIR digital filter and returns the filter coefficients in length N+1 vector B
FREQZ: Digital filter frequency response.
[H, W] = FREQZ(B,A,N) returns the N-point complex frequency response vector H and the
N-point frequency vector W in radians/sample of the filter
ANGLE: Phase angle.
ANGLE(H) returns the phase angles, in radians, of a matrix with complex elements.
HANN: Hanning window.
HANN(N) returns the N-point symmetric Hanning window in a column vector.
GRID: Grid lines.
GRID ON: adds major grid lines to the current axes.
HAMMING: Hamming window.
HAMMING(N) returns the N-point symmetric Hamming window in a column vector.
RECTWIN: Rectangular window.
W = RECTWIN(N) returns the N-point rectangular window.
KAISERORD: FIR order estimator (lowpass, highpass, bandpass, and multiband).
[N,Wn,BTA,FILTYPE] = KAISERORD(F,A,DEV,Fs) is the approximate order N,
normalized frequency band edges Wn, Kaiser window beta parameter BTA and filter type
FILTYPE to be used by the FIR1 function: B = FIR1(N, Wn, FILTYPE, kaiser( N+1,BTA ),
'noscale' ), F vector of band edge frequencies in Hz in ascending order between 0 and half the
sampling frequency Fs, DEV is the vector of maximum deviation or ripples allowable for
each band.
PLOT: Linear plot. PLOT(X, Y) plots vector Y versus vector X. If X or Y is a matrix then
the vector is plotted versus the rows or columns of the matrix, whichever line up.
PROGRAM
clear all;
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close all;
clc ;
% Kaiser Window
%pass band ripple = 0.087dB
%stop band attenuation = 60dB
%pass band edge frequency = 0.4π rad/sec
%stop band edge frequency = 0.6π rad/sec
%sampling frequency = 100 rad/sec
fs = 100; %rad/sec, sampling frequency
pf = 0.4*pi; %rad/sec, pass band frequency
sf = 0.6*pi; %rad/sec, stop band frequency
fsamp = fs/(2*pi); % fs into hertz
pf1 = pf/(2*pi); % pf into hetz
sf1 = sf/(2*pi); % sf into hertz
d1 = 10^(-0.05*60); %stop band ripple
d2 = (10^(0.05*0.087)-1)/(10^(0.05*0.087)+1); %pass band ripple
fcuts = [pf1 sf1]; %pass and stop band cut off frequency
mags = [1 0]; %magnitude assigning
%d3 = min(d1,d2);
devs = [d2 d1]; %setting deviation
w = 0:0.01:pi;
%to get the order n, kaiser window beta parameter BTA and filter type
[n,Wn,beta,ftype] = kaiserord(fcuts,mags,devs,fs);
%filter design using windows
h = fir1(n,Wn,ftype,kaiser(n+1,beta),'noscale');
[H,f] = freqz(h,1,w); % frequency response and frequency vector
gain = 20*log10(abs(H));
a = angle(H);
%PLOTTING THE GRAPHS
subplot(2,1,1);
plot(f/pi, gain); grid on;
title(' Magnitude Response of Kaiser Window');
xlabel(' Normalised Frequency');
ylabel (' Gain in DB');
subplot(2,1,2);
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plot(f/pi, a); grid on;
title(„ Phase Response of Kaiser Window „);
xlabel(' Normalised Frequency');
ylabel(' Angle');
%hanning,hamming and rectangular window
%pass band ripple = 0.4dB
%stop band attenuation = 44dB
%pass band edge frequency = 3000Hz
%stop band edge frequency = 2000Hz
%sampling frequency = 8000Hz
fsamp = 8000; %sampling frequency
fcuts = [2000 3000]; %pass band and stopband edge frequency
mags = [0 1]; %magnitude
d1 = 10^(-0.05*44); %stop band ripple
d2 = (10^(0.05*0.1)-1)/(10^(0.05*0.1)+1); %pass band ripple
devs = [d2 d1]; %setting deviation
W = 0:0.01:pi;
[n,Wn,beta,ftype] = kaiserord(fcuts,mags,devs,fsamp); %to get the order
% hanning window
h = hann(n+1);
b = fir1(n,Wn,h);
w = 0:0.01:pi;
[H,f] = freqz(b,1,w);
gain = 20*log10(abs(H));
an = angle(H);
%plotting magnitude and phase response of hanning window
figure;
subplot(2,1,1);
plot(f/pi, gain); grid on;
title('Magnitude Response Hanning Window');
xlabel('Normalised Frequency');
ylabel('Gain in dB');
subplot(2,1,2);
plot(f/pi, an); grid on;
title('Phase Response of Hanning Window');
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xlabel(' Normalised Frequency');
ylabel(' Angle');
% HAMMING WINDOW
h = hamming(n+1);
b = fir1(n,Wn,h);
w = 0:0.01:pi;
[H,f] = freqz(b,1,w);
gain = 20*log10(abs(H));
an = angle(H);
%plotting magnitude and phase response of hanning window
figure;
subplot(2,1,1);
plot(f/pi, gain); grid on;
title (' Magnitude Response of Hamming Window ');
xlabel(' Normalised Frequency');
ylabel (' Gain in dB');
subplot(2,1,2);
plot(f/pi, an); grid on;
title(' Phase Response of Hamming Window ');
xlabel (' Normalised Frequency');
ylabel(' Angle');
%RECTANGULAR WINDOW
h = rectwin(n+1);
b = fir1(n,Wn,h);
w = 0:0.01:pi;
[H,f] = freqz(b,1,w);
gain = 20*log10(abs(H));
an = angle(H);
%plotting magnitude and phase response of hanning window
figure;
subplot(2,1,1);
plot(f/pi,gain); grid on;
title (' Magnitude Response of Rectangular Window ');
xlabel (' Normalised Frequency');
ylabel (' Gain in dB');
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subplot(2,1,2);
plot (f/pi, an); grid on;
title ('Phase Response of Rectangular Window');
xlabel(' Normalised Frequency');
ylabel(' Angle');
OUTPUT
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Dept. Of ECE, SJCET, Palai 40
RESULT
The MATLAB program to design FIR filter and to plot the responses are executed and
output was verified.
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Dept. Of ECE, SJCET, Palai 41
DATE: 22-03-2011
EXPERIMENT NO: 11
IIR FILTER DESIGN
AIM
1. Write a MATLAB program to design Butterworth BPF with given specification and plot its
response
a. Pass band Ripple = 1.5 dB
b. Stop band attenuation = 20 dB
c. Pass band edge frequency = 800 Hz < f< 1000 Hz
d. Stop band edge frequency = 0 to 400 Hz and 2000Hz to infinity
e. Sampling Frequency = 8000 Hz
2. Write a MATLAB program to design Type -1 Chebyshev filter with given specification and plot its
response
a. Pass band Ripple = 0.5 dB
b. Stop band attenuation = 20 dB
c. Pass band edge frequency = 800Hz
d. Stop band edge frequency = 300Hz
e. Sampling Frequency = 3000 Hz
THEORY
The Butterworth filter is a type of signal processing filter designed to have as flat a frequency
response as possible in the pass band so that it is also termed a maximally flat magnitude filter.The
frequency response of the Butterworth filter is maximally flat (has no ripples) in the pass band and
rolls off towards zero in the stop band. When viewed on a logarithmic Bode plot the response slopes
off linearly towards negative infinity.
A first-order filter's response rolls off at −6 dB per octave (−20 dB per decade) (all first-order
low pass filters have the same normalized frequency response). A second-order filter decreases at −12
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dB per octave, a third-order at −18 dB and so on. Butterworth filters have a monotonically changing
magnitude function with ω, unlike other filter types that have non-monotonic ripple in the pass band
and/or the stop band.
Chebyshev filters are analog or digital filters having a steeper roll-off and more pass band
ripple (type I) or stop band ripple (type II) than Butterworth filters. Chebyshev filters have the
property that they minimize the error between the idealized and the actual filter characteristic over the
range of the filter, but with ripples in the pass band. Because of the pass band ripple inherent in
Chebyshev filters, filters which have a smoother response in the passband but a more irregular
response in the stop band are preferred for some applications.
These are the most common Chebyshev filters. The gain (or amplitude) response as a function of
angular frequency ω of the nth order low pass filter is
Where is the ripple factor, ω0 is the cut-off frequency and Tn() is a Chebyshev polynomial of
the nth order.
ALGORITHM
1. Start
2. Input the system parameters
3. Calculate the cut-off and order.
4. Design the Butterworth filter
5. Plot the magnitude and phase response
6. Design the Type-1 Chebyshev filter
7. Plot the magnitude and phase response
8. Stop
MATLAB FUNCTIONS USED
BUTTORD Butterworth filter order selection.
[N, Wn] = BUTTORD (Wp, Ws, Rp, Rs) returns the order N of the lowest order digital
Butterworth filter that loses no more than Rp dB in the passband and has at least Rs dB of
attenuation in the stop band. Wp and Ws are the passband and stop band edge frequencies,
normalized from 0 to 1 (where 1 corresponds to pi radians/sample)
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BUTTER Butterworth digital and analog filter design.
[B, A] = BUTTER (N, Wn) designs an Nth order low pass digital Butterworth filter and returns
the filter coefficients in length N+1 vectors B (numerator) and A (denominator). The coefficients
are listed in descending powers of z. The cutoff frequency Wn must be 0.0 < Wn < 1.0, with 1.0
corresponding to half the sample rate.
CHEBY1 Chebyshev Type I digital and analog filter design.
[B, A] = CHEBY1(N, R, Wp) designs an Nth order lowpass digital Chebyshev filter with R
decibels of peak-to-peak ripple in the passband. CHEBY1returns the filter coefficients in length
N+1 vectors B (numerator) andA (denominator). The passband-edge frequency Wp must be 0.0 <
Wp < 1.0 with 1.0 corresponding to half the sample rate.
CHEB1ORD Chebyshev Type I filter order selection.
[N, Wp] = CHEB1ORD (Wp, Ws, Rp, Rs) returns the order N of the lowest order digital
Chebyshev Type I filter that loses no more than Rp dB in the passband and has at least Rs dB of
attenuation in the stopband. Wp and Ws are the passband and stopband edge frequencies,
normalized from 0 to 1 (where 1 corresponds to pi radians/sample).
PROGRAM
%BUTTERWORTH BAND PASS FILTER
%pass band ripple = 1.5dB
%stop band attenuation = 20dB
%pass band frequency = 800Hz<= f <=1000Hz
%stop band frequency = 0 <= f <= 400Hz and 2000Hz <= f <= infinity
%sampling frequency = 8000Hz
clear all
close all
clc
rp = 1.5; % passband ripple
rs = 20; %stop band ripple
ft = 8000; %sampling frequency
wp1 = 2* 800/ft; %normalize passband edge frequencies
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wp2 = 2* 1000/ft;
wp = [wp1 wp2]; %pass band corner frequencies
ws1 = 2* 400/ft; %normalize stop band edge frequencies
ws2 = 2* 2000/ft;
ws = [ws1 ws2]; %stop band corner frequency
[n,Wn] = buttord(wp, ws, rp,rs); %to calculate order and cut off
[b,a] = butter (n, Wn); % to design bandpass filter coefficients
w = 0:0.01:pi;
freqz(b,a,w); % to plot magnitude and phase response
%CHEBYSHEV HIGHPASS FILTER
%pass band ripple = 0.5dB
%stop band attenuation = 20dB
%pass band edge frequency = 800Hz
%stop band edge frequency = 300Hz
%sampling frequency = 3000Hz
rp = 0.5; % passband ripple
rs = 20; %stop band ripple
ft = 3000; %sampling frequency
wp = 2* 800/ft; %normalize passband frequency
ws = 2* 300/ft; %normalize stop band frequency
[n,Wn] = cheb1ord(wp,ws,rp,rs); %returns order N and cut off
[b,a] = cheby1(n,rp,Wn,'high'); %designs an nth order high pass digital Chebyshev
filter
w = 0:0.01:pi;
figure;
freqz(b,a,w); % to plot magnitude and phase response
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OUTPUT
Butterworth filter
Chebyshev filter
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Dept. Of ECE, SJCET, Palai 46
RESULT
The MATLAB program to design a Butterworth band pass filter and type 1 Chebyshev
high pass filter has been executed and the filter responses are plotted.
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Dept. Of ECE, SJCET, Palai 47
DATE: 30-03-2011
EXPERIMENT NO: 12
FAMILIARIZATION OF VHDL
AIM
To familiarize the VHDL programming.
THEORY
VHDL is a hardware description language. It describes the behaviour of an electronic circuit
or system from which the physical circuit or system can then be attained (implemented). VHDL
stands for VHSIC Hardware Description Language. VHSIC is itself an abbreviation for Very High
Speed Integrated Circuits, an initiative funded by the United States Department of Defence in the
1980s that led to the creation of VHDL. Its first version was VHDL 87, later upgraded to the so called
VHDL 93.vHDL was the original and first hardware description language to be standardized by the
institute of electrical and Electronics Engineers through the IEEE 1076 standard. An additional
standard, the IEEE 1164, was later added to introduce a multi-valued logic system.
VHDL is intended for circuit synthesis as well as circuit simulation. However, though VHDL
is, fully simulateable, not all constructs are synthesizable.
A fundamental motivation to use VHDL (or its competitor, verilog) is that VHDL is a
standard, technology/vendor independent language, and is therefore portable and reusable. The two
main immediate applications of VHDL are in the field of programmable Logic Devices (including
CPLDs and FPGAs) and in the field of ASICs (Application Specific Integrated Circuits). Once the
VHDL code has been written, it can be used either to implement the circuit in a programmable device
(from Atera, Xilinx, Atmel etc) or can be submitted to a foundry for fabrication of an ASIC chip.
Currently, many complex commercial chips (microcontrollers, for example) are designed using such
an approach.
A final note regarding VHDL is that, contrary to regular computer programs which are
sequential, its statements are inherently concurrent parallel 0. for that reason, VHDL is usually
referred to as code rather than program. In VHDL, only statements placed inside a PROCESS,
FUNCTION, or PROCEDURE are executed sequentially.
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DESIGN FLOW
We start the design by writing the VHDL code, which is saved in a file with the extension
.vhd and the same name as its ENTITY's name. The first step in the synthesis process is compilation.
Compilation is the conversion of the high-level VHDL language, which describes the circuit at the
register Transfer level (RTL) into a netlist at the gate.
VHDL is a hardware description language that can be used to model a digital system. The
digital system can be as simple as a logic gate or as complex as a complete electronic system. A
hardware abstraction of this digital system is called an entity. This model specifies the external view
of the device and one or more internal views. The internal view of the device specifies the
functionality or structure, while the external view specifies the interface of the device through which
it communicates with the other models in its environment. Figure I.I shows the hardware device and
the corresponding software model. Figure 1.2 shows the VHDL view of a hardware device that has
multiple device models, with each device model representing one entity.
Netlist
(gate level)
(Gate
level) Optimized Netlist
(gatelevel)
Computation
Optimization
Simulation
Stimulation Physical Device
VHDL
enter (RTD Level)
( RTD level)
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To describe an entity, VHDL provides five different types of primary constructs, called"
design units. They are
1. Entity declaration
2. Architecture body
3. Configuration declaration
4. Package declaration
5. Package body
Entity declaration
An entity is modelled using an entity declaration and at least one architecture body. The entity
declaration describes the external view of the entity, for example, the input and output signal names.
The entity' declaration specifies the name of the entity being modelled and lists the set of interface
ports. Ports are signals through which the entity communicates with the other models in its external
environment.
Architecture body
The architecture body contains the internal description of the entity, for example, as a set of
interconnected components that represents the structure of the entity, or as a set of concurrent or
sequential statements that represents the behavior of the entity. Each style of representation can be
specified in a different architecture body or mixed within a single architecture body. The internal
details of an entity are specified by an architecture body using any of the following modeling styles:
1. As a set of interconnected components (to represent structure),
2. As a set of concurrent assignment statements (to represent dataflow),
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3. As a set of sequential assignment statements (to represent behavior),
4. Any combination of the above three.
The structural style of modelling describes only an interconnection of components without
implying any behaviour of the components themselves, nor of the entity that they collectively
represent. In data flow style of modelling , the flow of data through the entity is expressed primarily
using concurrent signal assignment statements. The structure of the entity is not explicitly specified in
this modelling style, but it can be implicitly deduced. The behavioural style of modelling specifies the
behaviour of an entity as a set of statements that are executed sequentially in the specified order. This
set of sequential statements, that are specified inside a process statement, do not explicitly specify the
structure of the entity but merely specifies its functionality. A process statement is a concurrent
statement that can appear within an architecture body. It is possible to mix the three modelling styles
that we have seen so far in a single architecture body. That is, within an architecture body, we could
use component instantiation statements (that represent structure), concurrent signal assignment
statements (that represent dataflow), and process statements (that represent behaviour).
Configuration declaration
A configuration declaration is used to create a configuration for an entity. It specifies the
binding of one architecture body from the many architecture bodies that may be associated with the
entity. It may also specify the bindings of components used in the selected architecture body to other
entities. An entity may have any number of different configurations.
Package declaration
A package declaration encapsulates a set of related declarations such as type declarations,
subtype declarations, and subprogram declarations that can be shared across two or more design units.
Package body
A package body is primarily used to store the definitions of functions and procedures that
were declared in the corresponding package declaration, and also the complete constant declarations
for any deferred constants that appear in the package declaration. Therefore, a package body is always
associated with a package declaration; furthermore, a package declaration can have at most one
package body associated with it. Contrast this with an architecture body and an entity declaration
where multiple architecture bodies may be associated with a single entity declaration.
Library declaration
In Library, the various definition group to use in VHDL is declared.
Generally, the declaration of the standard logic which is prescribed in the IEEE is specified.
There is various declaration but it seems OK if declaring the following 2 lines.
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library ieee;
use ieee.std_logic_1164.all;
The above declares all definitions which are prescribed in STD_LOGIC_1164 of the IEEE.
When using Xilinx Project Navigator, these declare statements are already written when making a
source file newly. When you design the more complicated circuit, more declaration must be done.
When using an arithmetic operation in the processing STD_LOGIC_UNSIGNED must be
specified.
use ieee.std_logic_unsigned.all;
Entity statements
In Entity, a port declaration, an attribute declaration, a generic declaration and so on are
written. When Entity ends, it writes END. The entity name behind end can be omitted.
Below, I will explain a port declaration and an attribute declaration.
Entity and architecture declaration
entity entity-name is
port (signal-names : mode signal-type;
signal-names : mode signal-type;
…
signal-names : mode signal-type);
end entity-names;
architecture architecture-name of entity-name is
type declarations
signal declarations
constant declarations
function definitions
procedure definitions
component declarations
begin
concurrent-statement
…
concurrent-statement
end architecture-name;
RESULT
The VHDL programming is familiarized.
Systems Lab
Dept. Of ECE, SJCET, Palai 52
DATE: 30-03-2011
EXPERIMENT NO: 13
LOGIC GATES
AIM
Write a VHDL program for generating waveforms of various logic gates.
THEORY
AND gate
An AND gate may have two or more inputs but only one output. The output of an AND gate
is 1 if and only if all the inputs are 1. Its logical equation is given by
C = A . B
Truth Table
OR gate
An OR gate may have two or more inputs but only one output. The output of an OR gate is
one if and only if one or more inputs are 1. Its logical equation is given by
C = A + B
Systems Lab
Dept. Of ECE, SJCET, Palai 53
Truth Table
NOT gate
A NOT gate, also called an inverter, has only one input and only one output. The
output of a NOT gate assumes the logic 1 state when its input is in logic 0 state and assumes the logic
0 state when its input is in logic 1 state.
Truth Table
NAND gate
NAND gate is a combination of an AND gate and a NOT gate. The output is a logic 0 level,
only when each of the inputs assumes logic 1 level. For any other combination of inputs, the output is
logic 1 level.
Systems Lab
Dept. Of ECE, SJCET, Palai 54
Truth Table
NOR gate
NOR gate is a combination of an OR gate and a NOT gate. The output is logic 1
level, only when each of its inputs assumes a logic 0 level. For any other combination of inputs, the
output is logic 0 level.
Truth Table
XOR gate
The XOR operation is widely used in digital circuits. The output of XOR gate is logic 0 when
both the inputs are same and the output is logic 1 when the inputs are not same.
Systems Lab
Dept. Of ECE, SJCET, Palai 55
Truth Table
XNOR gate
An XNOR gate is a combination of an XOR gate and a NOT gate. The XNOR gate is a two
input, one output logic, whose output assumes a 1 state only when both the inputs assumes a logic 0
state and the other a 1 state.
Truth Table
Systems Lab
Dept. Of ECE, SJCET, Palai 56
PROCEDURE
1. Create a new work space.
2. Create new file
3. Choose vhdl source
4. Enter name of source file and name of entity
5. Enter inputs and outputs.
6. Enter the program
7. Compile
8. Initialize simulation
9. Add simulators and generate waveform
10. End simulation
PROGRAM
library IEEE;
use IEEE.STD_LOGIC_1164.all;
entityentity_logicgate is
port(
a : in STD_LOGIC;
b : in STD_LOGIC;
c_or : out STD_LOGIC;
c_and : out STD_LOGIC;
c_nor : out STD_LOGIC;
c_nand : out STD_LOGIC;
c_xor : out STD_LOGIC;
c_not : out STD_LOGIC
);
endentity_logicgate;
architecturearch_logicgate of entity_logicgate is
begin
c_or <= a or b;
c_and <= a and b;
c_nor <= a nor b;
c_nand <= a nand b;
Systems Lab
Dept. Of ECE, SJCET, Palai 57
c_xor <= a xor b;
c_not <= not b;
endarch_logicgate;
WAVEFORMS:
RESULT
The VHDL programs for logic gates are executed correctly and output waveforms are plotted.
Systems Lab
Dept. Of ECE, SJCET, Palai 58
DATE: 30-03-2011
EXPERIMENT NO: 14
HALF ADDER AND FULL ADDER
AIM
To write a program for half adder and full adder in VHDL.
THEORY
1. HALF ADDER
A half adder is a circuit that adds two binary digits, giving a sum bit and a carry bit.
Sum, S=A ̅+B ̅=A B
Carry, C =AB
Truth table
OUTPUTS
A B SUM CARRY
0 0 0 0
0 1 1 0
1 0 1 0
1 1 1 1
2. FULL ADDER
A full adder is an arithmetic circuit that adds two bits and outputs a sum bit and a carry bit.
When adding two binary numbers each having two or more bits the LSBs can be added using a half
adder. The carry resulted from the addition of the LSBs is carried to the next significant column and
added to the two bits in that column. The full adder adds the bits A and B and the carry from the
previous column called carry_in, Cin and outputs the sum bit S and the carry bit called the carry_out
Cout.
Sum=A B C
Carry, Cout=AB+ACin+BCin
Systems Lab
Dept. Of ECE, SJCET, Palai 59
Truth table
OUTPUTS
A B C SUM CARRY
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1
PROCEDURE
1. Create new workspace
2. Create new file
3. Choose vhdl source
4. Enter name of source file and name of entity
5. Enter inputs and outputs
6. Enter the program
7. Compile
8. Initialize simulation
9. Add simulators and generate waveform
10. End simulation
PROGRAM
library IEEE;
use IEEE.STD_LOGIC_1164.all;
entity adder is
port(
a : in STD_LOGIC;
b : in STD_LOGIC;
c : in STD_LOGIC;
sum_half : out STD_LOGIC;
sum_full : out STD_LOGIC;
c_half : out STD_LOGIC;
c_full : out STD_LOGIC
);
Systems Lab
Dept. Of ECE, SJCET, Palai 60
end adder;
architecture behaviour of adder is
begin
sum_half <= a xor b;
c_half <= a and b;
sum_full <= a xor b xor c ;
c_full <= (a and b) or ( a and c) or (b and c);
end behaviour;
WAVEFORMS
RESULT
Half adder and full adder are implemented using VHDL and output waveforms are plotted.
Systems Lab
Dept. Of ECE, SJCET, Palai 61
DATE: 30-03-2011
EXPERIMENT NO.: 15
FLIP FLOPS
AIM
To write VHDL program for implementing the following flip flops.
D flip flop
T flip flop
JK flip flop
SR flip flop
THEORY
Flipflop, which is made up of an assembly of logic gates, is a memory element. A logic gate
by itself has no storage capability, but when connected together in ways permits the information to be
stored. A flipflop known as bistable multivibrator has two states. It can remain in either of the twp
states indefinitely. Its state can be changed by applying the proper triggering signal.
SR Flipflop
S-R flipflop is the simplest type of flip flop. It has two outputs labelled Q and ̅ and
two inputs labelled S and R. The state of the flipflop corresponds to the level of Q (high or low, 1 or
0) and ̅ the compliment of the state. Q0 represents the state of the flipflop before applying the inputs.
The name S-R or SET- RESET is derived from the names of its inputs.
Truth Table
INPUTS OUTPUT COMMENTS
S R Q
0 0 Q0 No change
0 1 0 RESET
1 0 1 SET
1 1 U Invalid
JK Flipflop
JK flipflop is very versatile and most widely used. The functioning of JK is similar to that of
SR flipflop, except that it has no invalid state as in SR When J=K=1, the flipflop toggles.
Systems Lab
Dept. Of ECE, SJCET, Palai 62
Truth table
INPUTS OUTPUT COMMENTS
J K Q
0 0 Q0 No Change
0 1 0 RESET
1 0 1 SET
1 1 ̅0 Toggle
D Flipflop
The edge triggered D flip-flop has only one input terminal. The D flipflop may be
obtained from SR by just putting one inverter between the S and R terminals. The single input to the
D flipflop is called the data input. The level present at D will be stored in the flipflop at the instant the
positive going transition occurs.
Truth Table
INPUT OUTPUT COMMENTS
D Q
0 0 RESET
1 1 SET
T Flipflop
A T flipflop has a single control input, labelled T for toggle. When T is HIGH, the
flip-flop toggles on every new clock pulse. When T is LOW, the flip flop remains in whatever state it
was before. T flipflop is obtained by connecting the J and K inputs to JK flipflop together.
Truth Table
INPUT OUTPUT COMMENTS
T Q
0 Q0 No Change
1 ̅0 Toggle
Systems Lab
Dept. Of ECE, SJCET, Palai 63
PROCEDURE
1. Create new workspace
2. Create new file
3. Choose VHDL source
4. Enter name of source file and name of entity
5. Enter inputs and outputs
6. Enter the program
7. Compile
8. Initialize simulation
9. Add simulators and generate waveform
10. End simulation
PROGRAM
library IEEE;
use IEEE.STD_LOGIC_1164.all;
entityff is
port(
d : in STD_LOGIC;
t : in STD_LOGIC;
s : in STD_LOGIC;
r : in STD_LOGIC;
j : in STD_LOGIC;
k : in STD_LOGIC;
clk : in STD_LOGIC;
rst : in STD_LOGIC;
dout : out STD_LOGIC;
tout : inout STD_LOGIC;
srout : inout STD_LOGIC;
jkout : inout STD_LOGIC
);
endff;
Systems Lab
Dept. Of ECE, SJCET, Palai 64
architecture behaviour of ff is
begin
process(clk,d,rst)
begin
caserst is
when '0' =>
if (clk 'event and clk = '1') then
dout<= d;
end if;
when '1' => dout <= '0';
when others => null;
end case;
end process;
-- T FLIPFLOP
process (t, clk)
begin
caserst is
when '0' =>
if(clk' event and clk = '1' and t = '0')then
tout<= tout;
elsif ( clk' event and clk = '1' and t = '1') then
tout<= not tout;
end if;
when '1' => tout <= '0';
when others => null;
end case;
end process;
-- J K FLIPFLOP
Process (j, k, clk,rst)
begin
caserst is
when '0' =>
if(clk' event and clk = '1' and j = '0' and k = '0') then
jkout<= jkout;
elsif(clk' event and clk = '1' and j = '0' and k = '1') then
Systems Lab
Dept. Of ECE, SJCET, Palai 65
jkout<= '0';
elsif(clk' event and clk = '1' and j = '1' and k = '0') then
jkout<= '1';
elsif(clk' event and clk = '1' and j = '1' and k = '1') then
jkout<= not jkout;
end if;
when '1' => jkout <= '0';
when others => null;
end case;
end process;
-- S R FLIPFLOP
process (s, r, clk,rst)
begin
caserst is
when '0' =>
if (clk' event and clk = '1' and s = '0' and r = '0') then
srout<= srout;
elsif (clk' event and clk = '1' and s = '0' and r = '1') then
srout<= '0';
elsif (clk' event and clk = '1' and s = '1' and r = '0') then
srout<= '1';
elsif(clk' event and clk = '1' and s = '1' and r = '1') then
srout<= '1';
end if;
when '1' => srout <= '0';
when others => null;
end case;
end process;
end behaviour;
Systems Lab
Dept. Of ECE, SJCET, Palai 66
WAVEFORMS
RESULT
All the flipflops are implemented using VHDL and output waveforms are plotted.
Systems Lab
Dept. Of ECE, SJCET, Palai 67
DATE: 30-03-2011
EXPERIMENT NO: 16
COMPARATOR
AIM
To design a comparator using VHDL
THEORY
A comparator is a logic circuit used to compare the magnitude of two binary numbers.
Depending on the design, it may either simply provide an output that is active when the two numbers
are equal or additionally provide outputs that signify which of the numbers is greater when equality
does not hold. Two binary numbers are equal, if and only if all their corresponding bits coincide. For
example, two 4-bit numbers, A3A2A1A0 and B3B2B1B0 are equal, if and only if A3= B3, A2= B2,
A1= B1 and A0= B0.
PROCEDURE
1. Create new workspace.
2. Create new file.
3. Choose vhdl source.
4. Enter name of source file and name of entity.
5. Enter inputs and outputs.
6. Enter the program.
7. Compile.
8. Initialize simulation.
9. Add simulators and generate waveform.
10. End simulation.
PROGRAM
library IEEE;
use IEEE.STD_LOGIC_1164.all;
entity comparator is
port(
a : in STD_LOGIC_VECTOR(2 downto 0);
b : in STD_LOGIC_VECTOR(2 downto 0);
Systems Lab
Dept. Of ECE, SJCET, Palai 68
c : out STD_LOGIC_VECTOR(1 downto 0)
);
end comparator;
architecture behaviour of comparator is
begin
process(a,b)
begin
if(a>b)then
c<="00";
elsif(a<b)then
c<="01";
elsif(a=b)then
c<="11";
end if;
end process;
end behaviour;
WAVEFORM
RESULT
The VHDL program for comparator is executed correctly and the waveform obtained while
simulation is plotted.