Lab Manual Ec-603 Dsp

DIGITAL SIGNAL PROCESSING

EC-603

EXPERIMENT1

AIM:

PROGRAM FOR THE GENERATION OF UNIT IMPULSE SIGNAL.

PROGRAM:

clc; clear all; close all;

t = 2:1:2;

y = [zeros (1, 2), ones (1, 1), zeros(1,2) ]; subplot (2, 2, 1); stem (t, y);

ylabel ( 'Amplitude ');→

xlabel (' (a) n ');→

BI LAB MANUAL AND WORKBOOK 6

LAB MANUAL AND WORK BOOK


EC-603

VIVA VOCE

Ques1 What do you mean by signal ?

AnsA signal is defined as a information containing message.

Ques2 Explain classification of the signals.

Ans 1. Deterministic & non deterministic,

2. Periodic & aperiodic,

3. Even & odd signal,

4. Causal & non causal signal,

5. Energy & Power Signal.

Ques3 Explain classification of the systems.

Ans 1. Static & dynamic,

2. Linear & non linear ,

3. Time invariant & time variant

4. Causal & non causal

5. Stable & unstable.

Ques4 Discuss the applications of digital signal processing.

Ans 1. Telecommunication,

2. Military,

3. Consumer Electronics,

4. Image processing,

5. Speech processing,




EC-603

6. Medicine.

7. Spectrum analysis.

Ques What do you mean by deterministic signal ?

Ans The nature and amplitude of such signal at any time can be predicted.




EC-603

EXPERIMENT 2

AIM:

PROGRAM FOR COMPUTING CIRCULAR CONVOLUTION.

PROGRAM:

clc;

close all;

clear all;

g = input (' enter the first sequence');

h = input (' enter the 2nd sequence ');

N1 = length (g);

N2 = length (h);

N = max (N1, N2 ) ;

N3 = N1 N2;

% Loop for getting equal length sequence

if (N3 = 0)

h = [h, zeros (1,N3 )];

else

g = [g, zeros (1,N3 )];

end

% Computation of circular convolved sequence

for n =1: N,

Y(n) = 0




EC-603 for I =1: N,

j = n – I + 1;

if (j = = 0)

j=N + j;

end

y(n) = y(n) + g(i) *h ( j);

end

end

disp ( 'The resultant signal is ' ); y

EXAMPLE:

enter the first Sequence [1 2 4]

enter the 2nd sequence [1 2 ]

The resultant signal is

y =1 4 8 8




EC-603

VIVA VOCE

Ques1 What do you mean by periodic signal ?

Ans A periodic signal repeats after a fixed time period.

Ques2 What do you mean by even signal ?

Ans A even signal satisfies even symmetry.

Ques3 What do you mean by odd signal ?

Ans A odd signal satisfies odd symmetry.

Ques4 What do you mean by causal signal ?

Ans A signal is said to be causal, if its amplitude is zero for negative time.

Ques What do you mean by noncausal signal ?

Ans A signal is said to be noncausal, if its amplitude is zero for positive time.




EC-603

EXPERIMENT3

AIM:

PROGRAM FOR COMPUTING DISCRETE FOURIER TRANSFORM.

ALGORITHM:

Get the signal x(n) of length N in matrix form

Get the N value

The transformed signal is denoted as

PROGRAM:

clc; close all; clear all ;

x = input ('enter the sequence ');

n = input ('enter the length of fft ');

X(k) = fft (x,n);

stem (y); y label ( 'imaginary axis >' );

xlabel( 'Real axis—>' );

X(k)

EXAMPLE:

enter the sequence [0 1 2 3 4 5 6 7]

enter the length of fft 8

X(k) =

Columns 1 through 4

28.0000 – 4.0000 + 9.6569i – 4.0000 + 4.0000i + 4.0000 + 1.6569i

Columns 5 through 8




EC-603 4.0000 – 4.0000 – 1.6569i – 4.0000 – 4.0000i – 4.0000 9.6569i

The eight point decimationin time fast Fourier transform of the sequence x(n) is computed using matlab

program and the resultant output is plotted in fig 15.6




EC-603

VIVA VOCE

Ques1 What do you mean by energy signal ?

Ans The energy signal is one, which has finite energy and zero average power.

Ques2 What do you mean by power signal ?

Ans The power signal is one, which has finite average power and infinite energy.

Ques3 What do you mean by static system ?

Ans The output of a static system at any specific time depends on the the input at that particular

time. It does not depends on the past or future value of the input.

Ques4 What do you mean by dynamic system ?

Ans The output of a dynamic system at any specific time depends on the the input at that specific

time and at other times also.

Ques What do you mean by linear system ?

Ans A linear system is one, which follows the super position theorem.




EC-603

EXPERIMENT4

AIM:

PROGRAM FOR THE DESIGN OF BUTTER WORTH ANALOG LOW PASS FILTER.

ALGORITHM:

Get the passband and stopband ripples,

Get the passband and stopband edge frequencies,

Get the sampling frequency,

Calculate the order of the filter using Equ 8.46,

Find the filter coefficient,

Draw the magnitude and phase response,

PROGRAM :

clc;

close all; clear all ;

format long

rp = input ( 'enter the passband ripple' );

rs = input ( 'enter the stopband ripple' );

wp = input ( 'enter the pass band freq' );

ws = input ( 'enter the stopband freq' );

fs = input ( 'enter the sampling freq' );

w1 = 2*wp/fs; w2= 2 *ws/ fs;

[n, wn] = buttord ( w1, w2, rp, rs, 's ' );

[z, p, k]= butter (n, wn);




EC-603 [b, a] = zp2tf ( z, p, k );

[b, a] =butter (n, wn, ' s');

w= 0: 0.01: pi;

[h, om]= freqs (b, a, w);

m = 20*log 10 (abs (h));

an = angle (h);

subplot (2, 1, 1); plot (om/pi, m);

ylabel ( 'Gain in db >' ); xlabel (' (a) Normalised frequency >');

subplot (2, 1, 2 ); plot (om/pi, an);

xlabel (' (b) Normalised frequency >');

ylabel (' phase in radians > ');

EXAMPLE:

enter the passband ripple 0.15

enter the stopband ripple 60

enter the passband freq 1500

enter the stopband freq 3000

enter the sampling freq 7000

The amplitude and phase response of the Butterworth low pass analog filter are shown in fig 15.7




EC-603

VIVA VOCE

Ques1 What do you mean by non linear system ?

Ans A non linear system is one, which does not follow the super position theorem.

Ques2 What do you mean by time invariant system ?

Ans A time invariant system is one, whose input output relationship does not vary with time. It is a

fixed system.

Ques3 What do you mean by time variant system ?

Ans A time variant system is one, whose input output relationship varies with time.

Ques4 What do you mean by causal system ?

Ans The response of the causal system to an input does not depend on future values of the input. It

depends only on the present and/or past values of the input.

Ques5 What do you mean by non causal system ?

Ans The response of the non causal system to an input depends on future values of the input as well

as on the present and/or past values of the input.




EC-603

EXPERIMENT5

AIM:

PROGRAM FOR THE DESIGN OF BUTTERWORTH ANALOG HIGHPASS FILTER.

PROGRAM:

clc;

close all; clear all;

format long

rp=input ('enter the passband ripple');

rs=input ('enter the stopband ripple');

wp= input(' enter the passband freq');

ws= input(' enter the stopband freq');

fs=input ('enter the sampling freq ');

w1 =2*wp /fs ; w2 =2*ws/fs ;

[n, wn] = buttord (w1, w2, rp, rs, 's');

[b, a] = butter (n, wn, 'high' ,'s');

w = 0: .01: pi;

[h,om] = freqs (b,a,w);

m = 20*log 10 (abs (h));

an = angle (h)

subplot (2, 1, 1); plot (om/pi,m);

ylabel ( 'Gain in dB >'); xlabel ( '(a) Normalised frequency >');

subplot (2 ,1 ,2 ); plot (om/pi,an );




EC-603xlabel ( '(b) Normalised frequency > ');

ylabel ( 'phase in radians >');

EXAMPLE:


enter the stopband ripple 40

enter the passband freq 2000

enter the stopband freq 3500


The amplitude and phase response of butterworth high pass analog filter are shown in fig




EC-603

VIVA VOCE

Ques1 What do you mean by stable system ?

Ans A system is said to be boundedinput, boundedoutput (BIBO) stable, if every bounded input

produces a bounded output.

Ques2 What do you mean by unstable system ?

Ans A system is said to be unstable system, if it does not follows the BIBO criteria.

Ques3 Explain the z transform.

Ans The z transform gives a method for analysis of discrete time system in the frequency domain.

Ques4 Explain the region of convergence (ROC).

Ans The set of z values in the z – plane for which the magnitude of X(z) is finite, is called as region

of convergence (ROC).

Ques5 Explain the properties of region of convergence (ROC).

Ans 1. The ROC does not contains any poles.

2. when x(n) is of finite duration, then the ROC is the entire z plane, except z = 0.




EC-603

EXPERIMENT6

AIM:

PROGRAM FOR THE DESIGN OF BUTTER WORTH ANALOG BANDPASS FILTER.

ALGORITHM:




Calculate the order of the filter using equation,

Find the filter coefficients,

Draw the magnitude and phase responses,

PROGRAMME:

clc ;


format long

rp = input ( ' enter the passband ripple . . . ');

rs = input ( 'enter the stopband ripple . . . ');

wp = input ( 'enter the passband freq. . . ');

ws = input ( 'enter the stopband freq. . . ');

fs = input( 'enter the sampling freq . . . ');

w1 = 2*wp/fs; w2=2*ws/fs;

[n] = buttord (w1,w2,rp, rs);

wn = [w1 w2 ];




EC-603 [b,a] = butter (n, wn, 'bandpass', ' s');

w = 0: .01: pi;

[h,om] = freqs (b, a, w);

m = 20*log 10 (abs (h));

an = angle (h);

subplot( 2, 1, 1); plot (om/pi, m);

ylabel ( 'Gain in db >'); xlabel ( '(a) Normalized frequency >');

Subplot (2, 1, 2); plot (om/pi, an);

xlabel ( '(b) Normalized frequency >');

ylabel ( 'phase in radians >');

EXAMPLE:

enter the pass band ripple . . . 0.36

enter the stop band ripple . . . 36

enter the passband freq . . . 1500

enter the stop band freq . . . 2000

enter the sampling freq . . . 6000

The amplitude and phase responses of Butterworth bandpass analog filter are shown in Fig




EC-603

VIVA VOCE

Ques1 Explain the properties of z – transform.

Ans 1. Linearity

2. Time reversal

3. Time shifting

4. Time scaling

5. Differentiation

6. Convolution

7. Correlation

8. Initial & Final value theorem

9. Time advance.

Ques2 Write the methods for inverse z transform.

Ans 1. Long division

2. Partial fraction expansion

3. Residue method.

Ques3 Explain the properties of DSP.

Ans 1. Linearity

2. Time invariance

3. Causality

4. Stability

Ques4 Explain the properties of convolution.

Ans 1. Commutative law

2. Associative law

3. Distributive law

Ques5 What do you mean by infinite impulse response (IIR) system.




EC-603

Ans An LTI system is said to be an IIR system, if its unit sample response h(n) is of infinite

duration.




EC-603

EXPERIMENT 7

AIM:

PROGRAM FOR THE DESIGN OF BUTTERWORTH ANALOG BANDSTOP FILTER.

ALGORITHM:




Calculate the order of the filter using Equation,

Find the filter coefficients,

Draw the magnitude and phase responses,

PROGRAM:

clc :


format long

rp = input ( 'enter the pass band ripple . . . ');

rs = input ( 'enter the stop band ripple . . .');

wp = input ( ' enter the passband freq . . . ');

ws = input ( ' enter the stopband freq . . .');

fs = input ( 'enter the sampling freq. . .');

w1 = 2*wp/fs ; w2= 2*ws/fs;

[n] = buttord (w1, w2, rp, rs, 's');

wn = [ w1 w2];




EC-603 [b,a] = butter (n, wn, 'stop', 's');

w = 0: .01: pi;

[h, om] = freqs (b, a, w);

m = 20*log 10 (abs (h));

an = angle (h);

subplot (2, 1, 1); plot (om/pi, m);

ylabel ( 'Gain in db >'); xlabel ( '(a) Normalized frequency >');

subplot (2, 1, 2); plot (om/pi, an);

xlabel ( '(b) Normalized frequency >');

ylabel ('phase in radians >');

EXAMPLE:

enter the passband ripple . . . 0.28

enter the stop band ripple . . . 28

enter the passband freq . . . 1000

enter the stopband freq . . . 1400

enter the sampling freq . . . 5000

The amplitude and phase response of Butterworth band stop analog filter are shown in Fig




EC-603

VIVA VOCE

Ques1 What do you mean by finite impulse response (FIR) system.

Ans An LTI system is said to be an FIR system, if its unit sample response h(n) is of finite duration.

Ques2 What do you mean by Discrete Fourier Transform (DFT).

Ans The Discrete Fourier transform computes the values of the z – transform for evenly spaced

points around the unit circle for a given sequence.

Ques3 Explain the properties of DFT.

Ans 1. Linearity

2. Periodicity

3. Shifting

4. Convolution

5. Time reversal

6. Circular time shift

7. Circular frequency shift

8. Circular convolution

9. Circular correlation

10. Parseval's theorem

Ques4 What do you mean by Fast Fourier Transform (FFT).

Ans The FFT is an algorithm that efficiently computes the DFT using graphical method.

Ques5 Explain method for computing FFT.

Ans 1. Decimation – in – Time (DIT)

2. Decimation – in – Frequency (DIF)




EC-603

EXPERIMENT 8

AIM:

PROGRAM FOR THE DESIGN OF FIR LOW PASS PASS, HIGH PASS, BAND PASS AND BAND

STOP FILTER USING HAMMING WINDOW.

ALGORITHM:




Calculate the order of the filter,

Find the window coefficient using equation,

Draw the magnitude and phase response,

PROGRAMME:

clc; clear all; close all ;

rp = input ('enter the passband ripple');

rs = input ('enter the stopband ripple');

fp = input(' enter the passband freq');

fs = input(' enter the stopband freq');

f = input(' enter the sampling freq');

wp = 2* fp/ f ; ws =2* fs /f;

num = 20*log10 (sqrt(rp*rs))13;

dem = 14.6 * (fs – fp) / f;

n = ceil( num / dem);




EC-603n1 = n+1;

if (rem (n,2 ) = 0)

n1 = n;

n = n1;

end

y = hamming (n1);

% low pass filter

b = fir1(n, wp, y);

[h,o] = freqz (b, 1, 256);

m = 20*log 10(abs(h));

subplot (2, 2, 1); plot (o/pi,m ); ylabel ('Gain in dB >');

Xlabel ('(a) Normalised frequency>');

% High pass filter

b = fir1 (n, wp, 'high', y);

[h,0] = freqz (b, 1, 256 );

m = 20*log10 (abs(h));

subplot (2, 2, 2); plot( o/pi,m ); ylabel ('Gain in db>');

xlabel ('(b) Normalised frequency>');

% Bandpass filter

wn = [ wp ws];

b = fir1 (n, wn, y);

[h,o]= freqz (b, 1, 256 );




EC-603m = 20* log10 (abs( h ));

subplot (2, 2, 3); plot( o/pi,m ); ylabel(' Gain in dB>');

xlabel ('(c) Normalised frequency>');

%Bandstop filter

b = fir1 (n, wn, 'stop', y);

[h,o]= freqz (b, 1, 256 );

m = 20* log10 (abs( h ));

subplot (2, 2, 4); plot( o/pi,m ); ylabel(' Gain in dB>');

xlabel ('(d) Normalized frequency>');

EXAMPLE:


enter the stop band ripple 0.01

enter the pass band freq 1200

enter the stop band freq 1700


The gain response of low pass,high pass band pass bandstop filter using Hamming window are shown in

fig




EC-603

VIVA VOCE

Ques1 Explain method for IIR filter design.

Ans 1. Approximation of derivatives

2. Impulse invariant

3. Bilinear transformation

Ques2 Explain basic structure for IIR systems.

Ans 1. Direct form I

2. Direct form II

3. Cascade realization

4. Parallel realization

Ques3 Explain windows techniques.

Ans 1. Rectangular

2. Hamming

3. Hanning

4. Blackman

5. Bartlett

6. Kaiser

Ques4 Explain the types of analog filters.

Ans 1. Low pass filter (LPF)

2. High pass filter (HPF)

3. Band pass filter (BPF)

4. Band stop filter (BSF)

Ques5 Write advantages of FIR filters over IIR filters.




EC-603

Ans 1. They are always stable.

2. the design methods are linear.

3. They can have an exact linear phase.

4. They can be realized efficiently in hardware.



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Lab Manual Ec-603 Dsp

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