SIDDHARTH INSTITUTE OF ENGINEERING &TECHNOLOGY:: PUTTURELECTRICAL & ELECTRONICS ENGINEERING

DIGITAL SIGNAL PROCESSINGQUESTION BANK

UNIT-I

Introduction

1 a). Determine the linear convolution for the two sequences x(n)=3,2,1,2,h(n)= 1,2,1,2 [L1][CO1][7M] b). Explain the power signal and Energy signal [L2][CO1][5M]

2) Find the forced response of the system described by the difference equation: [L4][CO1][12M]y(n)+ 2y(n-1)+y(n-2)=x(n)+x(n-1) for input x(n) =(-1)n u(n)

3 a). Find impulse response of the system described by the difference equation [L4][CO1][6M] y(n)+ y(n-1)-2y(n-2)= x(n-1)+2x(n-2).

b). Find 4-point DFT of the sequence x(n)=1,6,4,3 [L3][CO1][6M]

4) State and prove following properties of DFT [L2][CO1][12M]

i) Linearity ii) Circular time shifting iii) Circular frequency shifting iv) Time reversal v) Complex conjugate.

5 a). Determine the circular convolution for the two sequences x1(n)=1,2,3,4, x2(n)= 1,5,1,3 using concentric circles method. [L3][CO1][7M]

b). Explain the classification of discrete-time signals [L1][CO1][5M]

6 a). Find the natural response of the system described by the difference equation:

y(n)+ 2y(n-1)+y(n-2)=x(n)+x(n-1) with initial conditions y(-1)=y(-2)=1. [L4][CO1][8M] b) Justify how DFT can used as a linear Transform. [L2][CO1][4M]

7) Find the output y(n) of a filter whose impulse response is h(n)=[1,-1] and input x(n)= [1,-2,2,-1,3,- 4,4,-3]

using i) overlap add method ii)overlap-save method [L3][CO1][12M]

8) For each of the following systems, determine whether or not the system is static/dynamic, linear/non-linear, time variant/invariant, causal/ non-causal, stable/unstable. [L2][CO1][12M]

i) y(n)=cos[x(n)] ii) y(n)= x(-n+2)

9a). Explain frequency analysis of discrete-time systems. [L4][CO1][6M]

b). Determine magnitude and phase response for the system described by the difference equation:

y(n)=

12 x(n)+x(n-1)+

12 x(n-2) [L4][CO1][6M]

10a). Find 8 point DFT of the sequence x(n)=[1,2,1,0,2,3,0,1] [L3][CO1][7M]

b). Describe the relation between i) DFT to Z- transform ii) DFT to Fourier Series. [L2][CO1][5M]

UNIT-II

Fast Fourier Transform Algorithm

1) Compute 8-point DFT of the sequence x(n)= 1,2,3,4,4,3,2,1 using radix-2 DIT-FFT Algorithm. [L3][CO2][12M]

2a). Construct Radix-4 DIF FFT algorithm with neat sketch. [L2][CO2][7M]b). Compare DFT and FFT algorithms. [L2][CO2][5M]

3) Compute 8-point DFT of the sequence x(n)= 1,2,1,2,1,2,2,1 using radix-2 DIF-FFT Algorithm. [L3][CO2][12M]

4 a). Construct the decimation in time FFT algorithm with butterfly diagram. [L3][CO2][7M] b). Explain use of FFT in linear filtering and correlation. [L2][CO2][5M]

5 a). Explain decimation in frequency FFT algorithm. [L2][CO2][7M] b). Compare radix-2 DIT-FFT and DIF-FFT algorithms. [L2][CO2][5M]

6) Compute IDFT of the sequence x(n)= 7,-0.707-j0.707,-j, 0.707-j0.707,1, 0.707+j0.707,j,-0.707+j0.707. [L3][CO2][12M]

7) Formulate the DFT by divide and conquer approach [L2][CO2][12M]8) How do you compute DFT using [L3][CO2][12M]

a) The Goertzel Algorithm b) The chrip-z Transform

9 a). Explain Radix-4 FFT algorithm in decimation in time domain. [L2][CO2][7M] b). Describe Quantization errors in the direct computation of DFT. [L2][CO2][5M]

10 a). With a neat sketch find 4 point DFT of the sequence x(n)=[1,6,7,4] using radix2 DIT-FFT algorithm. [L3][CO2][8M]

b). Interpret the applications of FFT algorithm. [L2][CO2][4M]

UNIT-III

Implementation of Discrete-Time Systems

1 (a). Discuss frequency sampling structure for FIR filter. [L1][CO3][6M]

(b). Realize FIR filter with system function in cascade form [L4][CO3][6M]

H (z) = 1 +

52 z-1+2z-2+2z-3

2. Consider the system y (n) = y(n - 1) + 2y(n - 2) + x(n)+3x(n-1) [L4][CO3][12M](i) Find H(z) (ii) Realize using direct form-I and direct form-II.

3 (a). Obtain direct form-I,direct form-II,cascade,parallel form realization of following system: y(n) = 0.75y(n-1)-0.125y(n-2)+3x(n)+7x(n-1)+x(n-2) [L3][CO3][12M]

4. A system is represented by a transfer function H(Z) =3+

4 Z

Z−12 -

2

Z− 14 [L2][CO3][12M]

i) Does this system function H(Z) represent FIR or IIR.Justify?

ii) Give a difference equation for direct form-I structure.iii) Draw the block diagram for direct form-II and give equations for implementation.

5 (a). Differentiate the different structures for IIR systems [L3][CO3][5M] (b) Realize following system with difference equation in cascade form [L4][CO3][7M]

y(n)= y (n - 1) + 2y (n - 2) + x(n)-x(n-1)

6 (a). Explain lattice & lattice-ladder structure for IIR digital filter. [L2][CO3][6M] (b). Discuss transposed structures. [L1][CO3][6M]

7. The transfer function of a discrete causal system is given as H(Z)=

1−Z−1

1−0 . 2Z−1−0.15 Z−2[L3][CO3][12M]

i) Find difference equation ii) Draw cascade & parallel realizationsiii)Calculate impulse response of the system.

8. Realize system with following difference equation [L4][CO3][12M] y(n) = (3/4) y(n-1) – (1/8) y(n-2) + x(n) + (1/3) x(n-1). a) Cascade form b) Parallel form

9. a). Illustrate the realization of the IIR filter in cascade form [L2][CO3][6M]

(b). Explain representation of structures using signal flow graphs. [L2][CO3][6M]

10 (a). Explain conversion from lattice structure to direct form. [L4][CO3][6M]

(b). Determine the direct form realization of FIR with system function [L3][CO3][6M]

H(Z)= 1+2Z-1-3Z-2-4Z-3+5Z-4

UNIT –IV

Design of IIR Filters

1. (a).The analog transfer function H(s)= 2/(s+1)(s+2) Determine H(z) using impulse invariance method[L3][CO4][7M]

(b) Compare FIR and IIR filters. [L2][CO4][5M]

2. (a) Explain the features of Chebyshev approximation. [L1][CO4][6M] (b) Discuss the location of poles for Chebyshev filter. [L1][CO4][6M]3. (a) Discuss the characterization of IIR filter.. [L1][CO4][5M]

(b) Given specifications αp=1 dB; αs= 30dB; Ωp= 200rad/sec; Ωs=600 rad/sec. Determine the order the filter. [L3][CO4][7M]

4. (a) Compare features of different windowing functions. [L2][CO4][5M] (b) Determine the order and the pole of the low pass filter that has 3-dB attenuation at 500 Hz and an attenuation of

40 dB at 1000 Hz. [L3][CO4][7M]

5. Describe the IIR filter design approximation using Bilinear Transformation method. [L4][CO4][12M] Also sketch the s-plane to z-plane mapping. State its merits and demerits.

6. Using the bilinear transform, design a high pass filter, monotonic in pass band with cut off frequency of 100Hz and down 10dB at 350 H. the sampling frequency is 5000Hz. [L4][CO4][12M]

7. a). Discuss the frequency selective filters with plot. [L2][CO4][6M] b). Give the advantages and disadvantages of the digital filters [L1][CO4][6M]

8. Design a Chebyshev filter for the following specifications using [L4][CO4][12M]

a) Bilinear transformation b) Impulse invariant method 0.8≤H(ejw)≤1 0≤w≤0.2π H(ejw)≤0.2 0.6π≤w≤π 9. Describe the frequency transformation in digital filters [L2][CO4][12M]

10. a). Explain the frequency transformation in analog filters [L2][CO4][8M] b). Distinguish the Butterworth and Chebyshev filters [L2][CO4][4M]

UNIT – V Design of FIR Filters

1.Design an ideal HPF with desired frequency response Hd(ejw)= 1, п/4 ≤|w|≤п [L4][CO5][12M] 0, |w|≤ п/4

Find the values of h(n) for N=11 and also find H(Z) using Hanning window technique.

2. a). Determine the frequency response of the FIR filter defined by y(n)= 0.25x(n)+ x(n-1) + 0.25x(n-2). [L4][CO5][6M] b). Explain about the Rectangular window of the FIR filter. [L2][CO5][6M]

3. Design a ideal band pass filter with a frequency response Hd(ejw)=1, п/4 ≤|w|≤3п/4 = 0 otherwise Find the values of h(n)=11 and plot frequency response [L4][CO5][12M]

4 a) Design FIR filter using symmetric filter [L4][CO5][6M] b) Design a linear phase FIR filter using frequency sampling method. [L4][CO5][6M]

5. Design a filter with Hd(ej)= e-j3 -π/4≤≤π/4 [L4][CO5][12M] = 0 π/4≤≤π Using Hamming window with N = 7

6. a) Discuss about characteristics linear phase FIR filters [L2][CO5][6M] b) What are the effects of windowing? [L1][CO5][6M] 7.(a) Discuss about characteristics FIR filters. [L2][CO5][5M]

(b) What are the effects of windowing. [L1][CO5][7M]

8. Design a FIR low pass filter satisfying the following specifications αp≤0.1 dB; αs≥44.0 dB; p= 20rad/sec;s=600 rad/sec and sf=100rad /sec. [L4][CO5][12M]

9. A band pass FIR filter of length 7 is require. It is to have lower and upper cut off frequencies of 3kHz and is intended to be used with a sampling frequency of 24kHz. Determine the filter coefficients using hamming window. Consider the filter to be causal. [L3][CO5][12M]

10. Illustrates the followings a) Rectangular window [L2][CO5][4M] b) Hamming window [L2][CO5][4M] c) Hanning window [L2][CO5][4M]

SIDDHARTH GROUP OF INSTITUTIONS :: PUTTURSiddharth Nagar, Narayanavanam Road – 517583

QUESTION BANK (OBJECTIVE)

Subject with Code : Digital Signal Processing(16EC422 ) Course & Branch: B.Tech - EEE

Year & Sem: IV-B.Tech & I-Sem Regulation: R16

UNIT – IINTRODUCTION

1) Sequence steps for converting analog signal to digital signal ________________________2) Analog signal given to the sampler then the output is __________________3) ‘A signal that varies continually with time’ then the signal is ________________4) ‘A signal that has values at particular instant of time’ then the signal is ________________5) If X(n) is a signal and X(n+N)=X(n) then X(n) is said to be _________________6) If X(n) is a signal and X(n+N)≠X(n) then X(n) is said to be _________________7) If X(n) is a periodic signal and X(n+N)=X(n) then N is said to be ______________8) If X(n) is a signal and fallow the property X(-n)=X(n) then X(n) is said to be _______________9) If X(n) is a signal and fallow the property X(-n)= -X(n) then X(n) is said to be ______________10) A signal is defined as X(n)= 1 for n=0; and X(n)= 0 for n≠0; then X(n) is said to be ____________11) A signal is defined as X(n)= 1 for n≥0; and X(n)= 0 for n<0; then X(n) is said to be ____________12) A signal is defined as X(n)= n for n>0; and X(n)= 0 for n<0; then X(n) is said to be ____________13) If the energy of a signal X(n) is finite value then power of that signal is ____________14) If the energy of a signal X(n) is infinite then power of that signal is _____________15) If the system output depends only on present and past inputs,the system is said to be ___________16) If the system output depends on present, past and future inputs, the system is said to be __________17) If a system satisfies the superposition theorem then system is said to be ______________ system 18) If a relaxed system doesn’t satisfy the superposition theorem then system is said to be __________19) A LTI system is said to be stable if __________________ 20) ________ is example for linear signal 21) _______________ is alternate Method for processing analog signals 22) The Sequence of steps for converting analog signal to digital signal _______________ 23) _______________ is Operation on Independent Variable 24) _______________ is Operation on dependent Variable25) If x(n) is given signal then x(2n) Indicates _______________ 26) If x(n) is given signal then x(n/2) Indicates _______________ 27) _____________ is definition for unit sample sequence 28) _____________ is definition for unit step sequence 29) _____________ is the relation δ (n) in terms u(n) 30) _____________ is definition for Energy Signal 31) _____________ is definition for Power Signal 32) A signal is periodic signal with period ‘N’ if x(n) = ___________33) ________ is fundamental period of x(n) = cos (nπ/2) 34) A signal is said to be even signal if _____________35) A signal is said to be odd signal if ______________ 36) If x(n) is given signal then even part of x(n) is ___________37) If x(n) is given signal then odd part of x(n) is ___________38) A signal is said to be causal signal if _____________ 39) A System is said to be causal system if present output depends _____________

40) DFS is a mathematical tool used to analyze _____________

UNIT – IIFAST FOURIER TRANSFORM ALGORITHM (FFTA)

1) In N-Point DITFFT, number of butterflies per stage is ____________

2) In 16-Point DITFFT, each sample represented by ___________ digits

3) In N-Point DIT-FFT input sequence order is ____________

4) In N-Point DIT-FFT, number of stages in the flow graph is _________

5) In N-Point DITFFT, output sequence order is ____________

6) Direct DFT requires__________ number of complex multiplications7) FFT algorithms requires __________ number of complex multiplications 8) In DITFFT, Inputs/outputs for each butterfly in stage ‘m’ separated by ___________ 9) In direct computation of DFT the number of real multiplications are ____________ 10) In direct computation of DFT the number of real additions are ____________ 11) In direct computation of DFT the number of complex additions are ___________ 12) In direct computation of DFT the number of complex multiplications are ____________ 13) In radix 2 FFT, the no of complex multiplications for ‘m’ stages is _____________ 14) In radix 2 FFT, the no of complex additions for ‘m’ stages is ______________ 15) For a 32 point DFT using direct method, no of complex additions are _____________ 16) For a 16 point DFT using direct method, no of complex multiplications are __________ 17) In 128 point FFT, the number of complex additions are ____________ 18) In 64 point FFT, the number of complex multiplications are _________ 19) The value of the twiddle factor at N=4 and n*k=3 is __________ 20) Complex multiplication takes place before add/sub operations in ___________ 21) Complex multiplication takes place after add/sub operations in ____________ 22) If X(k) consist of N- no of frequency samples, then its discrete frequency locations are given by the _______23) Twiddle factor WN given by __________

24) Symmetry property of twiddle factor is _________ 25) Periodicity property of twiddle factor is _________ 26) By using twiddle factor computational complexicity reduced from N2 to _____________ 27) The number of butterflies per stage is _____________ for N-point DFT 28) Bit reversal order for I/P of DITFFT algorithm is _____________ 29) Bit reversal order for O/P of DIFFFT algorithm is ____________30) The I/Ps and O/Ps for each butterfly in the stage ‘m’ is separated by _____________31) Computational complexity will__________by using twiddle factors in FFT calculation 32) How many twiddle factors are required for computing 8-point FFT ___________ 33) How many twiddle factors are required for computing 16-point FFT __________34) How many twiddle factors are required for computing 32-point FFT __________35) W8

0 value is __________

36) W81 value is __________

37) W82 value is __________

38) W83 value is __________

39) In 16 point DITFFT algorithm number of butterflies per stage is ____________40) In 8 point DITFFT algorithm number of butterflies per stage is _____________41) In 32 point DITFFT algorithm number of butterflies per stage is ____________ 42) In 4 point DITFFT algorithm number of butterflies per stage is _____________

UNIT – III

Implementation of discrete Time Systems

1) The three factors that influence structures are computation complexity, memory and _____________ 2) The unit sample response of FIR system is identical to _____________

3) The length of FIR filter is ____________

4) The direct form structure is equivalent to ______________ 5) The number of memory locations needed to realize direct form structure is _____________6) The number of additions per output point needed to realize direct form structure is __________ 7) The number of multiplications per output point in direct form structure is ___________8) The tapped delay line filter is also called as ______________

9) The condition for FIR system to have linear phase is _____________ 10) For a linear phase FIR system if M=even the no of multiplications is ________________ 11) For a linear phase FIR system if M=odd the no of multiplications is ________________

12) In frequency sampling structure the value used to characterize the filter is _____________ 13) The most efficient form of realization is _______________

14) The structure that is mostly used in digital speech processing is _______________15) IIR filter’s Direct form is obtained by cascading all zero system with ___________

16) In IIR direct form I the number of additions is ________

17) The no of memory locations needed to realize IIR direct form I is ________ 18) In IIR direct form I the number of multiplications is __________

19) The no of multiplications required to realize IIR direct form II is _______ 20) The Direct form structure is also called as _________

21) The no of additions required to realize IIR direct form II is _______ 22) The structure obtained by changing all branch direction and input & output is _____________ 23) The structure that needs lesser memory location is __________

24) The Parallel form realization of IIR system is obtained by __________

25) The Lattice coefficients are also called as ___________ 26) The Polar form of Z can be expressed as ____________

27) Z transform of sequence x(n)=1,0,3 is ____________

28) Z transform of sequence x(n)=1,1,3is ____________ ( take origin at second sample) 29) ROC for Left hand finite sequence is _____________

30) ROC for Right hand finite duration sequence is _____________

31) ROC for Left hand infinite duration sequence is _____________ 32) ROC for Right hand infinite duration sequence is ____________

33) The range of values of Z for which z-Transform converges called as ____________34) ROC for Two sided finite duration sequence is ________________ 35) Z-transform of unit sample sequence is _____________

36) Z-transform of δ (n-m) is ____________ 37) Z-transform of unit step sequence is __________

38) Z-transform of an u(n) is ___________

39) ROC for unit sample sequence is _______________

40) ROC for unit step sequence is _______________

UNIT – IVDesign of IIR Digital Filters

1. IIR Filters are ___________ type.

2. In the Impulse Invariance Transformation, relationship between Ω and ω is _______________

3. Non-linearity in the relationship between Ω and ω is known as ______________

4. In the Bilinear Transformation, the Relationship between Ω and ω is ____________

5. Butterworth filters have ________________

6. Chebyshev filters have _________________

7. Type-1 Chebyshev filters contains ___________________

8. Type-2 Chebyshev filter is also called __________________

9. The physically realizable IIR filters do not have _____________ phase

10. In ----------------------transformation, the impulse response of digital filter is the sampled version of the impulse of analog filter.

11. Aliasing occurs only in ___________ transformation.

12. In ______________ approximation, the magnitude response is equiripple in the Passband and monotonic in the stopband13. In _____________ approximation, the magnitude response is monotonic in the Passband and equiripple in the stopband14. In ____________ approximation, the magnitude response is maximally flat at the origin and monotonically decreases with increasing frequency15. At the cutoff frequency, the magnitude of the Butterworth filter is ___________times the maximum value16. The ideal filters are ___________17. In fourier series method to get transfer function of realizable filter, H(z) is to be multiplied by ________18. The abrupt truncation of Fourier series results in oscillations in __________19. The frequency of a digital filter is ____________20. For rectangular window, the main lobe width is equal to ____________21. For Hanning window, the main lobe width is equal to ______________22. For Hamming window, the main lobe width is equal to _____________23. For Blackman window, the main lobe width is equal to ______________24. For Kaiser Window, the main lobe width is equal to ________________25. For Rectangular window, the peak side lobe magnitude in dB is ____________26. For Hanning window, the peak side lobe magnitude in dB is ____________27. For Hamming window, the peak side lobe magnitude in dB is ____________28. For Blackman window, the peak side lobe magnitude in dB is ____________29. For a linear phase filter the delay is _____________30. In FIR filters, ____________ is a linear function of ω31. In ____________ window spectrum the higher side lobe attenuation is achieved at the expense of increased main lobe width32. In ____________ window spectrum the increase in side lobe attenuation is achieved at expense of constant attenuation at high frequencies33. In ____________ window spectrum has the highest attenuation for side lobes34. In ____________ window spectrum, the side lobe magnitude is variable35. In ____________ window spectrum, the width of the main lobe is triple that of Rectangular window for same value of N.36. In ____________ window spectrum, the width of the main lobe is double that of Rectangular window for same value of N.37. The __________ response of the filter is Fourier transform of impulse response of the filter.38. The ideal filters are ___________, and hence physically unrealizable39. In FIR filters with constant phase delay, the impulse response is ___________40. The generation of oscillations due to slow convergence of the Fourier series near the points of discontinuity is called __________ phenomenon

UNIT-VDesign of FIR filters

1.The number of additions per output point needed to realize direct form structure is ____________2.The number of multiplications per output point in direct form structure is ___________

3.The tapped delay line filter is also called as _____________ 4.The condition for FIR system to have linear phase is ____________5.For a linear phase FIR system if M=even the no of multiplications is ____________

6.For Hanning window ,windowing function is equal to _____________7.For Hamming window ,windowing function is equal to ____________ 8. __________ is the Z-transform for x(n-3)

9.For rectangular window ,the windowing function is equal to _____________10.For Hamming window , the value of α __________ 11.In FIR filters , ___________ is a linear function of ω 12. __________ is the Z-transform of y(n-3) 13.For Butterworth filters the poles are located at ____________14.The range of values of Z for which z-Transform converges called as ________________ 15. Z-transform of δ (n-m) is ______________ 16.FIR system is a ___________ 17. __________ type of system is called all pole system 18. For the given specification αs=6db, maximum allowable stop band(λ) ___________ 19.Warping effect is present in ______________ method 20.The phase of symmetric impulse response with odd length is given by ______________21. ____________ is a condition for asymmetric linear phase FIR filter with odd length22. For a stable filters all poles lies in_________ of s-plane 23. _________________ is another name for triangular windowing technique 24. _________________ methods are used for designing LPF and HPF 25. The _______________ response of the filter is fourier transform of impulse response.

26.The ideal IIR filters are ____________, and hence physically unrealizable 27.In FIR filters with constant phase delay, the impulse response is _____________ 28.The generation of oscillations due to slow convergence of the Fourier series near the Points of discontinuity is called __________ phenomenon 29.The FIR filters are ___________,and hence physically realizable 30. ____________________ is the difference equation of the FIR filter of length M, input x(n) and output y(n).31. The lower and upper limits on the convolution sum reflect________ and __________ characteristics of the filter.32. __________condition should the unit sample response of a FIR filter satisfy to have a linear phase.33. The roots of the polynomial H(z) are identical to the roots of the polynomial__________.34. The roots of the equation H(z) must occur in ________________ pairs.35. If the unit sample response h(n) of the filter is real, complex valued roots occur in _________ pairs.36. _________ is the value of h(M-1/2) if the unit sample response is anti-symmetric.37. ___________ is the number of filter coefficients that specify the frequency response for h(n) symmetric.38. ________is the number of filter coefficients that specify the frequency response for h(n) anti-symmetric.39. The anti-symmetric condition with M even is not used in the design of ___________linear-phase FIR filter.40. The ______________ condition is not used in the design of low pass linear phase FIR filter.