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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 ( )

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