EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
VALLIAMMAI ENGINEERING COLLEGE
SRM Nagar, Kattankulathur – 603203.
DEPARTMENT OF ELECTRONICS AND COMMUNICATION
ENGINEERING
QUESTION BANK
EC6502 PRINCIPLES OF DIGITAL SIGNAL PROCESSSING
III- YEAR V SEM
ACDEMIC YEAR: 2017-2018 ODD SEMESTER
Prepared by
Dr.N.USHA BHANU, Dr.J.MOHAN, Ms. S.SUBBULAKSHMI
Department of ECE
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur – 603 203.
DEPARTMENT OF ECE
QUESTION BANK
SUBJECT : EC6502 PRINCIPLES OF DIGITAL SIGNAL PROCESSSING
SEM / YEAR: V Sem III Year
UNIT I DISCRETE FOURIER TRANSFORM
Discrete Signals and Systems- A Review – Introduction to DFT – Properties of DFT – Circular Convolution -
Filtering methods based on DFT – FFT Algorithms –Decimation in time Algorithms, Decimation in frequency Algorithms – Use of FFT in Linear Filtering.
PART A
Q.No Questions BT
Level Competence
1. State DT system. BTL 1 Remembering
2. Define DFT and IDFT. BTL 1 Remembering
3. What is meant by bit reversal? BTL 1 Remembering
4. Mention zero padding. What are its uses? BTL 1 Remembering
5. Outline twiddle factor. BTL 1 Remembering
6. Recall Parseval’s relation with respect to DFT. BTL 1 Remembering
7. Compare the advantages of FFT over DFTs. BTL 2 Understanding
8. How many stages of decimations are required in the case of a 64 point
radix 2 DIT FFT algorithm?
BTL 2 Understanding
9. Illustrate in – place computation. BTL 2 Understanding
10. Write the differences and similarities between DIT and DIF? BTL 2 Understanding
11. Select the smallest number of DFTs and IDFTs needed to compute the
linear convolution of length 50 sequences with a length of 800 sequence
BTL 3 Applying
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
is to be computed using 64 point DFT & IDFT.
12. Identify the differences between Overlap – add and Overlap – save
method.
BTL 3 Applying
13. Draw the basic butterfly diagram for the computation in the decimation
in frequency FFT algorithm and explain.
BTL 3 Applying
14. Distinguish between linear convolution and circular convolution. BTL 4 Analyzing
15. List the linearity and convolution properties of DFT. BTL 4 Analyzing
16. Compare Radix 2 DIT, DIF FFT Algorithm. BTL 4 Analyzing
17. Determine the number of multiplications required in the computation of
8 – point DFT using FFT.
BTL 5 Evaluating
18. Evaluate the 4 – point DFT sequence x(n) = {1, 1, -1, -1}. BTL 5 Evaluating
19. Test the causality and stability of y(n) = sin x(n). BTL 6 Creating
20. Predict whether ℎ(𝑛) =−1
4𝛿(𝑛 + 1) +
1
2𝛿(𝑛) −
1
4𝛿(𝑛 − 1) is stable
and causal? Justify.
BTL 6 Creating
PART –B (16 Marks)
1. (i)With appropriate diagrams discuss how Overlap add and Overlap
save methods are used. (7)
(ii) Find the eight point DFT of the sequence
using radix – 2 DIT algorithm. (6)
BTL 1 Remembering
2. (i) Show that FFT algorithms help in reducing the number of
computations involved in DFT computation. (5)
(ii) Find a 8 point DFT of the sequence using DIT – FFT algorithm
(8)
BTL 1 Remembering
3. (i) Find the N – point DFT of the following sequences
(a) x(n) = δ(n) (b) x(n) = δ(n-1) (8)
BTL 1 Remembering
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
(ii) Derive the butterfly diagram of 8 point radix – 2 DIF FFT
algorithm and fully label it. (5)
4. (i) State and prove if 𝑥3(𝑘) = 𝑥1(𝑘)𝑥2(𝑘), then 𝑥3(𝑛) =
∑ 𝑥1(𝑚)𝑁−1𝑚=0 𝑥2((𝑛 − 𝑚))𝑁. (7)
(ii) Using the above equation, prove for the 8 point DFT of the
sequence 𝑥1(𝑛) = {1,1,1,1,0,0,0} and 𝑥2(𝑛) = {1,0,0,0,0,1,1,1}. (6)
BTL 1 Remembering
5. (i) Illustrate the construction of an 8-point DFT from two 4-point
DFTs. (7)
(ii) Illustrate the reduction of an 8-point DFT to two 4-point DFTs by
decimation in frequency. (6)
BTL 2 Understanding
6. (i) Explain Radix – 2 DIF FFT algorithm. Compare it with DIT – FFT
algorithms. (7)
(ii) Explain the following properties of DFT. (6)
a) Time reversal
b) Parseval’s theorem
BTL 2 Understanding
7. (i) Summarize the following properties of DFT (a) Linearity (b) (8)
Complex conjugate property (c) Circular Convolution (d) Time
Reversal. (8)
(ii) Summarize the difference between overlap – save method and
overlap – add method. (5)
BTL 2 Understanding
8. (i) Solve the DFT of the sequence whose values for one period is
given by x(n) = {1,1,-2,-2} (6)
(ii)Compute the eight point DFT of the sequence x(n)=
{1,2,3,4,4,3,2,1} using Radix-2 DIT algorithm. (7)
BTL 3 Applying
9. (i) Solve the IDFT of the sequence X(K)= {6, -2+2j, -2, -2-2j} using
Radix 2 DIF algorithm. (6)
(ii) Compute an 8 point DFT of the sequence (7)
BTL 3 Applying
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
10. (i) Examine whether the following systems are linear (7)
(1) 𝑦(𝑛) =1
𝑁∑ 𝑥(𝑛 − 𝑚)𝑁−1
𝑚=0
(2) 𝑦(𝑛) = [𝑥(𝑛)]2
(ii) Compute the DFT of x(n) = {1, 1, 0, 0} (6)
BTL 4 Analyzing
11. (i) Examine the transfer function and impulse response of the system.
𝑦(𝑛) −33
44𝑦(𝑛 − 1) +
11
88𝑦(𝑛 − 2) = 𝑥(𝑛) +
11
33𝑥(𝑛 − 1) (7)
(ii) Examine the convolution sum of
𝑥(𝑛) = {
1 , 𝑛 = −2,0,1
2, 𝑛 = −1
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
And ℎ(𝑛) = 𝛿(𝑛) − 𝛿(𝑛 − 1) + 𝛿(𝑛 − 2) − 𝛿(𝑛 − 3) (6)
BTL 4 Analyzing
12. (i) Compute the 8 point DFT for the following sequences using DIT –
FFT algorithm (7)
(ii) Compute 8 – point DFT of the sequence x(n) = {0, 1, 2, 3, 4,5, 6,
7} using radix – 2 DIF algorithm. (6)
BTL 4 Analyzing
13. (i) Compute the eight point DFT of the sequence by using the DIT and
DIF – FFT algorithm.
(7)
(ii) Determine the impulse response of the causal
System.
𝑦(𝑛) − 𝑦(𝑛 − 1) = 𝑥(𝑛) + 𝑥(𝑛 − 1) (6)
BTL 5 Evaluating
14. (i) Perform the linear convolution of the sequence x(n) = {1, -1, 1, -1}
and h(n) = {1,2,3,4} using DFT method. (7)
(ii) Estimate the linear convolution of finite duration sequences h(n) =
{1,2} and x(n) = {1, 2, -1, 2, 3, -2, -3, -1, 1, 1, 2, -1} by Overlap add
method? (6)
BTL 6 Creating
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
PART C
1. Evaluate radix 2 –DIT FFT algorithm and obtain DFT of the sequence
x(n) = {1,2,3,4,4,3,2,1} using DIT algorithm. (15)
BTL 5 Evaluating
2. (i) Compute IDFT of the sequence X(K) = {7,-0.707,-j0.707,-j,0.707-
j0.707,1,0.707 + j0.707 j,- 0.707 + j 0.707 } using DIF Algorithm. (8)
(ii) Perform the linear convolution of finite duration sequence (7)
h(n) = {1,2} and x(n) ={1,2,-1,2,3,-2,-3,-1,1,2,-1} by overlap save
method.
BTL 5 Evaluating
3. (i) Analyze the difference and similarities between DIT and DIF radix
2 FFT Algorithm. (8)
(ii) Compute the number of multiplication and additions used in a 64
point DFT. Also compare it with the computations required for
DIT/DIF algorithm. (7)
BTL 6 Creating
4. (i) Calculate the percentage of saving in calculation in computing a
512 point using radix 2 FFT when compared to direct DFT. (8)
(ii) Draw and explain the basic butterfly diagram of DIF FFT. (7)
BTL 6 Creating
UNIT II IIR FILTER DESIGN
Structures of IIR – Analog filter design – Discrete time IIR filter from analog filter – IIR filter design by Impulse
Invariance, Bilinear transformation, Approximation of derivatives – (LPF, HPF, BPF, BRF) filter design using frequency translation.
PART A
Q.No Questions BT
Level Competence
1. Discuss the need for prewarping. BTL 1 Remembering
2. List the properties of Chebyshev filter. BTL 1 Remembering
3. What is the advantage of direct form II realization when compared to direct form I realization?
BTL 1 Remembering
4. Mention the requirements for the digital filter to be stable and causal. BTL 1 Remembering
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
5. Write the properties of Butterworth filter? BTL 1 Remembering
6. What are the advantages and disadvantages of bilinear transformation? BTL 1 Remembering
7. Compare Butterworth with Chebyshev filters. BTL 2 Understanding
8. Mention the advantages of cascade realization. BTL 2 Understanding
9. Give the steps in design of a digital filter from analog filters. BTL 2 Understanding
10. Compare IIR and FIR filters. BTL 2 Understanding
11. Use the backward difference for the derivative to convert analog LPF with
system function 𝐻(𝑠) = 1
𝑆+2 .
BTL 3 Applying
12. Develop the Direct Form II representation of a Second order IIR system. BTL 3 Applying
13. Identify the expression for location of poles of normalized Butterworth filter.
BTL 3 Applying
14. Why do we go for analog approximation to design a digital filter? BTL 4 Analyzing
15. Justify why the Butterworth response is called a maximally flat response. BTL 4 Analyzing
16. Distinguish between recursive and non-recursive realization. BTL 4 Analyzing
17. Justify why impulse invariant method is not preferred in the design of IIR filer other than LPF?
BTL 5 Evaluating
18. Sketch the frequency response of an odd and even order Chebyshev low pass filters?
BTL 5 Evaluating
19. Compute H(z) for the IIR filter whose 𝐻(𝑠) =1
𝑠+6 with T=0.1Sec using
Bilinear transformation.
BTL 6 Creating
20. Convert the given analog transfer function 𝐻(𝑠) =1
𝑠+𝑎 into digital by
impulse invariant method.
BTL 6 Creating
PART B (16 Marks)
1. Find the system function H(z) of the Chebyshevs low pass digital filter with the specifications
=1dB ripple in the pass band 0
=15dB ripple in the stop band 0
using bilinear transformation assume T=1Sec) (13)
BTL 1 BTL 1
Remembering Remembering
2. If 𝐻𝑎 (𝑆) =1
(𝑆+1)(𝑆+2) , find the corresponding H(z) using impulse invariant
method for sampling frequency of 5 samples/Second. (13)
BTL 1
Remembering
3. (i) Choose an analog Butterworth filter that has a 2 dB pass band
attenuation at a frequency of 20 r/Sec & at least 10 dB stop band attenuation at 30 r/Sec? (6)
(ii) Find a low pass Butterworth digital filter with the following specification Ws= 4000, Wp= 3000
BTL 1 Remembering
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
Ap= 3 dB, As= 20 dB, T= 0.0001 Sec. (7)
4. (i) If 𝐻𝑎(𝑠) =2
(𝑆+1)(𝑠+2) , find the corresponding H(z) using impulse
invariant method. Assume T=1 Second. (7)
(ii) Obtain the cascade and parallel realizations for the system function
given by
𝐻(𝑧) = 1+ 𝑍−1
41
(1+ 𝑍−1)(1+ 𝑍−1+ 𝑍−2)41
21
21 (6)
BTL 1 Remembering
5. (i) Explain the procedure for designing analog filters using the Chebyshev approximation (6)
(ii) Convert the following analog transfer function in to digital using
impulse invariant mapping with T=1Sec
𝐻(𝑠) =3
(𝑆+3)(𝑆+5) (7)
BTL 2
BTL 2
Understanding
Understanding
6. (i) Explain the Bilinear transform method of IIR filter design. What is
warping effect? Explain the poles and zeros mapping procedure clearly.
(6)
(ii) Demonstrate a high pass filter with pass band cut off frequency of 1000
Hz and down 10 dB at 350 Hz the sampling frequency is 5000 Hz using
Bilinear Transformation. (7)
BTL 2
BTL 2
Understanding
Understanding
7. A system is represented by a transfer function H(z) is given by
H(z)= 3 + [ 4z/z-(1/2) ] – [ z/z-(1/4) ] a) Does this H (z) represent a FIR or IIR filter? (2)
b) Give a difference equation realization of this system using direct
form I. (6)
c) Draw the block diagram for the direct form 2 canonic realization
and give the governing equation for implementation. (5)
BTL 2 Understanding
8. (i) Develop a digital Butterworth filter using impulse invariance method satisfying the constraints Assume T=1Sec
0.8 ≤ |𝐻(𝑒𝑗𝑤)| ≤ 1 0 ≤ 𝑤 ≤ 0.2𝜋
|𝐻(𝑒𝑗𝑤)| ≤ 0.2 0.6𝜋 ≤ 𝑤 ≤ 𝜋 (7)
(ii) Obtain the direct form I direct form II and cascade form realization of the following system functions
y(n)=0.1y(n-1)+0.2y(n-2)+3x(n)+3.6x(n-1)+0.6x(n-2) (6)
BTL 3
BTL 3
Applying
Applying
9. (i) Construct the cascade form realization of the digital system
y(n)=3/4 y(n-1)- (1/8)y(n-2) +1/3x(n-1)+x(n) (6) (ii) Develop the given analog filter with transfer function
𝐻(𝑠) =2
(𝑆+1)(𝑠+2) into a digital IIR filter using bilinear
Transformation. Assume T=1Sec. (7)
BTL 3 Applying
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
10. (i) Examine the analog filter with system function 𝐻(𝑠) =𝑆+0.1
(𝑆+0.1)2+9 into a
digital filter IIR filter using Bilinear Transformation. The digital filter
should have resonant frequency of 𝑊𝑟 =𝜋
4 . (6)
(ii) A digital filter with a 3dB bandwidth of 0.25 π is to be designed from
analog filter whose system response is 𝐻(𝑠) =Ω𝐶
𝑆+Ω𝐶. Use bilinear
transformation and obtain H (z). (7)
BTL 4 Analyzing
11. Analyze a digital Chebyshev filter to satisfy the constraints
0.707 ≤ |𝐻(𝑒𝑗𝑤)| ≤ 1 0 ≤ 𝑤 ≤ 0.2𝜋
|𝐻(𝑒𝑗𝑤)| ≤ 0.1 0.5𝜋 ≤ 𝑤 ≤ 𝜋
using Bilinear transformation and assuming = 1𝑠𝑒𝑐 . (13)
BTL 4
Analyzing
12. Simplify the following pole – zero IIR filter into a lattice ladder structure.
𝐻(𝑧) =[1+2𝑧−1+2𝑧−2+𝑧−3]
[1+(13
24)𝑧−1+(
5
8)𝑧−2+(
1
3)𝑧−3]
. (13)
BTL 4 Analyzing
13. (i) Design a digital Second order low pass Butterworth filter with cut off frequency 2200 Hz using bilinear transformation. Sampling rate is 8000
Hz. (6)
(ii) Determine the cascade form and parallel form implementation of the
system governed by the transfer function (7)
𝐻(𝑠) =1+𝑍−1
1+2𝑍−1
BTL 5 Evaluating
14. (i) Convert the analog filter into a digital filter whose system function is
𝐻(𝑠) =𝑆 + 0.2
(𝑆 + 0.2)2 + 9
Use impulse invariance technique. Assume 𝑇 = 1𝑠𝑒𝑐. (6)
(ii) For the analog transfer function
𝐻(𝑠) =2
(𝑆 + 1)(𝑆 + 2)
Determine H (z) using impulse invariant method. Assume 𝑇 = 1𝑆𝑒𝑐. (7)
BTL 6
Creating
PART C
1 Design a third order Butterworth digital filter using impulse invariant
technique. Assume the sampling period T=1Sec (15)
BTL 6
Creating
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
2 Propose a digital Butterworth filter with the following specifications :
0.707 ≤ |𝐻(𝑒𝑗𝑤)| ≤ 1 0 ≤ 𝑤 ≤ 0.5𝜋
|𝐻(𝑒𝑗𝑤)| ≤ 0.2 0.75𝜋 ≤ 𝑤 ≤ 𝜋
using bilinear transformation determine system function H(z) assuming
𝑇 = 1𝑠𝑒𝑐 . (15)
BTL 6
Creating
3 (i) Determine the analog band pass filter with system function 𝐻(𝑠) =1
(𝑆+0.1)2+5 into a digital filter IIR filter using backward difference for the
derivative with sampling period T=0.1 Sec . (10)
(ii) An analog filter has a transfer function 𝐻(𝑠) =10
(𝑆2+7𝑆+10) .
Evaluate a digital filter equivalent to this using impulse invariant method
for T=0.2. (5)
BTL 5 Evaluating
4 Evaluate the direct form I, direct form II, cascade and parallel form realization of LTI system governed by the equation:
y(n)= −3
8 𝑦(𝑛 − 1) +
3
32 𝑦(𝑛 − 2) +
1
64 𝑦(𝑛 − 3) + 𝑥(𝑛) +
3𝑥(𝑛 − 1) + 2𝑥(𝑛 − 2) (15)
BTL 5 Evaluating
UNIT III FIR FILTER DESIGN
Structures of FIR – Linear phase FIR filter – Fourier Series - Filter design using windowing techniques
(Rectangular Window, Hamming Window, Hanning Window), Frequency sampling techniques – Finite word length effects in digital Filters: Errors, Limit Cycle, Noise Power Spectrum.
PART A
Q.No Questions BT
Level Competence
1. Define Gibbs Phenomenon.
BTL 1 Remembering
2. What are the desirable characteristics of window? BTL 1 Remembering
3. How would you define symmetric and antisymmetric FIR filters?
BTL 1 Remembering
4. List the features of FIR filter design using Kaiser’s approach?
BTL 1 Remembering
5. Find the techniques of designing FIR filters?
BTL 1 Remembering
6. Mention the features of FIR filter.
BTL 1 Remembering
7. Compare the advantages and disadvantages of FIR filter?
BTL 2 Understanding
8. Interpret the reasons that FIR filter is always stable?
BTL 2 Understanding
9. Why FIR filters are called as all zero filter? BTL 2 Understanding
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
10. Outline the principle of designing FIR filter using frequency sampling
method?
BTL 2 Understanding
11. Identify the properties of FIR filter?
BTL 3 Applying
12. Summarize the steps involved in FIR filter design. BTL 3 Applying
13. Develop the necessary and sufficient condition for linear phase
characteristic in FIR filter?
BTL 3 Applying
14. List the possible types of impulse response for linear phase FIR filters? BTL 4 Analyzing
15. Analyze the principle of designing FIR filter using windows?
BTL 4 Analyzing
16. Explain the desirable characteristics of the windows? BTL 4 Analyzing
17. Determine the transversal structure of the system function H(z) = 1 + 2Z-1 - 3Z-2 - 4Z-3
BTL 5 Evaluating
18. Interpret the effect of having abrupt discontinuity in frequency response of
FIR filters
BTL 5 Evaluating
19. Construct the direct form implementation of the FIR system having
difference equation. y(n) = x(n) – 2x(n-1) + 3x(n-2) – 10x(n-6)
BTL 6 Creating
20. Discuss the difference between Hamming window and Blackman Window. BTL 6 Creating
PART B (16 Marks) 1. Design a high pass filter with a frequency response
Find the values of h(n) for N = 11 using hamming window. Find H(z) and
determine the magnitude response. (13)
BTL 1 Remembering
2. (i) Show with neat sketches the implementation of FIR filters in direct
form and Lattice form. (6) (ii) Select a digital FIR band pass filter with lower cut off frequency 2000Hz
and upper cut off frequency 3200 Hz using Hamming window of length
N=7. Sampling rate is 10000 Hz. (7)
BTL 1 Remembering
3. (i) Determine the frequency response of FIR filter defined by
y(n) = 0.25x(n) + x(n – 1) + 0.25x(n – 2) (7) (ii) What are steps involved in designing of FIR filter using frequency
sampling method. (6)
BTL 1 Remembering
4. (i) List the steps involved by the general process of designing a digital filter. (7)
(ii) List the advantages of FIR filters. (6)
BTL 1 Remembering
5. (i) How would you design a FIR low pass filter having the following
specifications using Hanning window
BTL 2
Understanding
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
assume N = 7 (7) (ii)Illustrate FIR low pass digital filter using the frequency sampling method
for the following specifications
Cut off frequency = 1500Hz
Sampling frequency = 15000Hz Order of the filter N = 10
Filter Length required L = N+1 = 11 (6)
BTL 2
Understanding
6. (i) The transfer function 𝐻(𝑧) = ∑ ℎ(𝑛)𝑍−𝑛𝑀−1𝑁=0 characteristics a FIR filter
(M=11). Interpret the magnitude response. (8)
(ii) Use Fourier series method to design a low pass digital filter to
approximate the ideal specifications given by
𝐻(𝑒𝑗𝑤) = {1, |𝑓| ≤ 𝑓𝑝
0, 𝑓𝑝 < |𝑓| ≤𝐹
2
Where 𝑓𝑝 = pass band frequency
𝐹= sampling frequency (5)
BTL 2 Understanding
7. Demonstrate a filter with
𝐻𝑑(𝑒𝑗𝑤) = 𝑒−𝑗3𝑤 , −𝜋
4≤ 𝑤 ≤
𝜋
4
0, 𝜋
4< |𝑊| ≤ 𝜋
using a Hamming window with N=7. (13)
BTL 2 Understanding
8. Develop a FIR filter using hanning window with the following
specification .Assume N = 5.
(13)
BTL 3 Applying
9. (i) Using a rectangular window technique, design a low pass filter with pass
band gain of unity cut off frequency of 1000Hz and working at a sampling frequency of 5 kHz. The length of the impulse response should
be 7. (7) (ii) Consider an FIR lattice filter with coefficients k1 = 1/2; k2 = 1/3; k3 =
1/4.
Solve the FIR filter coefficients for the direct form structure. (6)
BTL 3 Applying
10. (i) Realize the system function by linear phase FIR structure
(7)
BTL 4 Analyzing
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
(ii) Analyze the steps in designing of FIR filters using windows? (6) 11. A low pass filte has the desired response as given below, examine the filter
co efficient h(n) for M=7,using type 1 frequency sampling technique.
𝐻𝑑(𝑒𝑗𝑤) = {𝑒−𝑗3𝑤 , 0 ≤ 𝜔 <
𝜋
2
0 ,𝜋
2≤ 𝜔 ≤ 𝜋
(13)
BTL 4 Analyzing
12. Consider the transfer function 𝐻(𝑧) = 𝐻1(𝑧). 𝐻2(𝑧) where 𝐻1(𝑧) =1
1−𝛼1𝑧−1
and 𝐻2(𝑧) =1
1−𝛼2𝑧−1 . Examine the output round off noise power by
assuming 𝛼1 = 0.5, 𝛼2 = 0.6. (13)
BTL 4 Analyzing
13. Determine the coefficients {h(n)} of a linear phase FIR filter of length
M = 15 which has a symmetric unit sample response and a frequency response that satisfies the condition
(7)
(ii) Obtain the linear phase realization of the system function (6)
BTL 5 Evaluating
14. Design an ideal high pass filter using Hanning Window with a frequency response .Assume N = 11.
(13)
BTL 6 Creating
PART C
1 Evaluate the filter coefficients of a linear phase FIR filter of length N= 15
which has a symmetric unit sample response and a frequency response that satisfies the condition
𝐻𝑟 (2𝛱𝑘
15) = 1 for k = 0, 1,2,3
0.4 for k=4 0 for k= 5,6,7 (15)
BTL 5 Evaluating
2 Determine the transfer function H(z) of an ideal band reject filter with a desired frequency response for N=11.
𝐻 𝑑(𝑒𝑗𝑤) = 1 𝑓𝑜𝑟 |𝜔| ≤𝛱
3𝑎𝑛𝑑 |𝜔| ≥
2𝛱
3 (15)
BTL 5 Evaluating
3 Design a band pass filter which approximates the ideal filter with cut off
frequencies at 0.2 rad/Sec and 0.3 rad/Sec. The order of the filter is N=7. Use Hamming window. (15)
BTL 6 Creating
4 Determine the transfer function and realization structure for linear phase FIR filter for the given specifications using Hamming window for N=7.
BTL 6 Creating
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
𝐻𝑑(𝑒𝑗𝑤) = {𝑒−𝑗3𝑤 , −
𝜋
6≤ 𝜔 <
𝜋
6
0 ,𝜋
6≤ |𝜔| ≤ 𝜋
(15)
UNIT IV FINITE WORDLENGTH EFFECTS
Fixed point and floating point number representations – ADC –Quantization- Truncation and Rounding errors -
Quantization noise – coefficient quantization error – Product quantization error - Overflow error – Roundoff noise power - limit cycle oscillations due to product round off and overflow errors – Principle of scaling
PART A
Q.No Questions BT Level Competence
1. Write two kinds of limit cycle behavior in DSP.
BTL 1 Remembering
2. List the two types of quantization employed in a digital system?
BTL 1 Remembering
3. What is quantization step size?
BTL 1 Remembering
4. Define Noise transfer function.
BTL 1 Remembering
5. Define dead band
BTL 1 Remembering
6. Label the advantages of floating point arithmetic.
BTL 1 Remembering
7. Describe the input quantization error.
BTL 2 Understanding
8. Explain block floating point representation? What are its advantages?
BTL 2 Understanding
9. Compare truncation with rounding errors. BTL 2 Understanding
10. Illustrate the methods used to prevent overflow.
BTL 2 Understanding
11. Identify the three-quantization errors in finite word length registers in
digital filters.
BTL 3 Applying
12. Organize the effects of product quantization error.
BTL 3 Applying
13. Build the truncation of data results in?
BTL 3 Applying
14. Distinguish between fixed point and floating point arithmetic.
BTL 4 Analyzing
15. Examine the representation for which truncation error is analyzed.
BTL 4 Analyzing
16. Why rounding is preferred to truncation in realizing digital filter? BTL 4 Analyzing
17. Explain product round off noise.
BTL 5 Evaluating
18. Interpret the relationship between steady state noise powers due to
quantization to the b bits representing the binary sequence?
BTL 5 Evaluating
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
19. Consider the truncation of negative numbers represented in (bs-b ) bits
be truncated. Obtain the range of truncation error for sign magnitude,
1’s complement and 2’s complement representation of the negative
numbers.
BTL 6 Creating
20. Justify the need for scaling in filter implementation. BTL 6 Creating
1. Explain in detail the errors resulting from rounding and truncation. (13) BTL 1 Remembering
2. Consider a Second order IIR filter with
Find the effect on quantization on pole locations of the given system
function in direct form and in cascade form. Assume b = 3 bits. (13)
BTL 1 Remembering
3. What is called quantization noise? Derive the expression for
quantization noise power. (13)
BTL 1 Remembering
4. Determine the limit cycle behavior of the following systems
(i) Y(n) = 0.7y(n-1) +x(n)
(ii) Y(n) = 0.65y(n-2)+0.52y(n-1)+x(n) Find the dead band effect of the above systems. (13)
BTL 1 Remembering
5. (i) Explain the limit cycle oscillations due to product round off and
overflow errors? (7)
(ii) Explain how reduction of product round-off error is achieved in
digital filters? (6)
BTL 2 Understanding
6. (i) Compare the truncation and rounding errors using fixed point and
floating point representation. (5)
ii). Represent the following numbers in floating point format with five
bits for mantissa and three bits for exponent. (8)
(a) 710
(b) 0.2510
(c) -710
(d) -0.2510
BTL 2 Understanding
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
7. (i).Explain the characteristics of limit cycle oscillation with respect to the
system described by the difference equation : y(n) = 0.95 y(n-1) + x (n) ;
x(n)= 0 and y(n-1)= 13. Determine the dead range of the system. (7)
(ii). Explain the effects of coefficient quantization in FIR filters. (6)
BTL 2 Understanding
8. With respect to finite word length effects in digital filters, with examples
discuss about
i). Over flow limit cycle oscillation (7)
ii). Signal scaling (6)
BTL 3 Applying
9. (i)Solve for the signal to quantization noise ratio of A/D converter. (7)
(ii) Compare the truncation and rounding errors using fixed point and
floating point representation. (6)
BTL 3 Applying
10. (i) Analyze the effects of co-efficient quantization in FIR filter? (6)
(ii) Distinguish between fixed point and floating point arithmetic. (7)
BTL 4
BTL 4
Analyzing
Analyzing
11. (i)The output of an ADC is applied to a digital filter with system
function (𝑧) =0.5𝑧
𝑧−0.5 . Find the output noise power from digital filter
when input signal is quantized to have 8 bits. (6)
(ii) Show that ∑ 𝑥2(𝑛) =1
2𝜋𝑗∮ 𝑥(𝑧)𝑥(𝑧−1)𝑧−1𝑑𝑧∞
𝑛=0 in a closed
integral. (7)
BTL 4
BTL 4
Analyzing
Analyzing
12. Examine the dead band of the system y(n) = 0.2y(n – 1) + 0.5y(n – 2) +
x(n)Assume 8 bits are used for signal representation. (13)
BTL 4 BTL 4
Analyzing Analyzing
13. Explain the characteristics of limit cycle oscillation with respect to the
system described by the difference equation 𝑦(𝑛) = 0.95𝑦(𝑛 − 1) +
𝑥(𝑛). Determine the dead band of the filter. (13)
BTL 5
BTL 5
Evaluating
Evaluating
14. Draw the quantization noise model for a Second order system
𝐻(𝑧) =1
1−2𝑟 cos 𝜃𝑧−1+𝑟2𝑧−2 and estimate the steady state output noise
variance. (13)
BTL 6
BTL 6
Creating
Creating
Part C
1. Consider the transfer function 𝐻(𝑧) = 𝐻1(𝑧)𝐻2(𝑧) where
𝐻1(𝑧) = 1
1−𝑎1𝑧−1 and 𝐻2(𝑧) =
1
1−𝑎2𝑧−1 find the output round off
noise power. Assume 𝑎1 = 0.5 and 𝑎2 = 0.6 and find output round off
noise
power. (15)
BTL6 Creating
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
2. The output signal of an A/D converter is passed through a first order low
pass filter, with transfer function given by
𝐻(𝑧) = (1−𝑎)𝑧
𝑧−𝑎for 0 < a < 1.
Find the steady state output noise power due to quantization at the output
of digital filter. (15)
BTL6 Creating
3. Given 𝐻(𝑍) =
0.5+0.4𝑍−1
1−0.312𝑍−1 is transfer function of a digital filter find the
scaling factor 𝑆𝑜to avoid overflow in adder 1 of digital filter shown in
figure (15)
BTL5 Evaluating
4. The input to the system y (n) = 0.999y(n-1) + x(n) is applied to an ADC.
What is the power produced by the quantization noise at the output of the
filter, if the input is quantized to (i) 8 bits. (ii) 16 bits. (15)
BTL5 Evaluating
UNIT V DSP APPLICATIONS
Multirate signal processing: Decimation, Interpolation, Sampling rate conversion by a rational factor – Adaptive
Filters: Introduction, Applications of adaptive filtering to equalization.
PART A
Q.No Questions BT
Level Competence
1. Show the need for anti aliasing filter.
BTL 1 Remembering
2. Tell about decimation in multi rate signal processing.
BTL 1 Remembering
3. What is Sub band coding?
BTL 1 Remembering
4. Recall the echo cancellation multi rate signal Processing.
BTL 1 Remembering
5. Define multi rate signal processing.
BTL 1 Remembering
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
6. Tell about down sampling and up sampling of multi rate signal Processing. BTL 1 Remembering
7. State sampling theorem for a band limited signal BTL 2 Understanding
8. State the various applications of adaptive filters BTL 2 Understanding
9. Outline and express the anti – imaging filter.
BTL 2 Understanding
10. Write down the frequency response of up sampler? BTL 2 Understanding
11. Build the direct form representation of adaptive filters?
BTL 3 Applying
12. Construct the symbolic representation of an interpolator and decimator.
BTL 3 Applying
13. Give the applications of multi rate DSP.
BTL 3 Applying
14. Examine the areas in which multirate processing is used.
BTL 4 Analyzing
15. Describe the steps involved in adapting filtering. BTL 4 Analyzing
16. Classify the commonly used adaptive algorithms? BTL 4 Analyzing
17. Discuss the decimator. If the input to the decimator is x(n) = {1,2,-
1,4,0,5,3,2}. What is the output? BTL 5 Evaluating
18. Explain the advantages of multi rate processing.
BTL 5 Evaluating
19.
Develop the expression for the following multi rate system.
BTL 6 Creating
20. If the spectrum of a sequence x(n) is X(ejω), then what is the spectrum of a
signal down sampled by a factor 2?
BTL 6 Creating
PART B (16 Marks)
1. (i) Draw the signal flow graph for IIR structures M-to-1 decimator. (7)
(ii) Draw the signal flow graph for 1-to-L interpolator. (6) BTL 1 Remembering
2. For the signal x(n), obtain the spectrum of down sampled signal x(Mn) and
upsampled signal x(n/L). (13) BTL 1 Remembering
3. Discuss in detail about any two applications of adaptive filtering with a
suitable diagram. (13) BTL 1 Remembering
4. What are the procedures to implement digital filter bank using multi rate
signal processing? (13) BTL 1 Remembering
5. Illustrate the poly phase structure of decimator and interpolator?
(13)
BTL 2 Understanding
6.
(i) Summarize the various applications of adaptive filters? (6)
(ii) State the applications of multirate signal processing? (7) BTL 2 Understanding
7. (i) Explain the design of narrow band filter using sampling rate
conversion. (7) BTL 2 Understanding
4 2 4 6
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
(ii) Show the design steps involved in the implementation of multistage
sampling rate converter. (6)
8.
A signal x(n) is given by x(n) = {0,1,2,3,4,5,6,0,1,2,3….} (13)
i) Obtain the decimated signal with a factor of 2.
ii) Obtain the interpolated signal with a factor of 2.
BTL 3 Applying
9.
i). Obtain the decimated signal y(n) by a factor 3 from the input signal
x(n). (5)
ii). Implement a 2-stage decimator for the following specification. (8)
Sampling rate of the input signal =20 kHz, M=100.
Pass band= 0 to 40 Hz
Transition band = 40 to 50 Hz
Pass band ripple = 0.01
Stop band ripple = 0.002.
BTL 3 Applying
10.
List the applications of adaptive filters in:
a. Echo cancellation (7)
b. Equalization. (6)
BTL 4 Analyzing
11.
i). Analyze the efficient transversal structure for decimator and
interpolator? (8)
ii).What are the applications of MDSP in sub band coding of signals? (5)
BTL 4 Analyzing
12. Examine sampling rate conversion by a rational factor and derive input
and output relation in both time and frequency domain. (13) BTL 4 Analyzing
13.
Implement a two stage decimator for the following specifications. (13)
Sampling rate of the input signal= 20,000Hz. M=100
Passband=0 to 40 Hz Transition band = 40 to 50 Hz.
Pass band ripple = 0.01 Stop band ripple= 0.002.
BTL 5 Evaluating
14. For the multi rate system shown in figure, formulate the relation between
x(n) and y(n). (13) BTL 6 Creating
EC6502_PDSP_2018-Dr.N.Usha Bhanu, Dr.J.Mohan, S.Subbulakshmi
PART C
1
For the multirate systems show in figure, develop an expression for the
output as function of the input x(n) (15)
BTL 6 Creating
2
(i) For the given data sequence x(n) = {1,4,6,8,10,12,13,2,3,15,5}, find the
output sequence which is down-sampled version x(n)by
(i) 2. (ii) 3. (iii) 4. (9)
(ii). For the sequence x(n) = {5,6,8,4,2,1,3,12,10,7,11}. Find the output of
sequence Y(Z) which is down-sampled version of x(n) by 2 (6)
BTL 5 Evaluating
3
(i) Discuss the points to be observed form multirate signal processing
using the operation of up sample and down sample. (5)
(ii) Explain a short note on subband coding on multirate signal
processing. (10)
BTL 5 Evaluating
4
(i) Develop the principle of adaptive filter and derive the expression of
normalized filter regularized MSE. (8)
𝐽𝑚𝑆𝑚𝑖𝑛=𝜎𝑑 2 (𝑛) − 𝑃𝑇(𝑛)𝑅𝑥𝑥
−1p(n).
(ii) Estimate the adaptive filter work as equalizer give the relevant
mathematical expression. (7)
BTL 6 Creating
2
2
2
2
Z - 1
Z - 1
y ( n )
x n ( )