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BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI

FIRST SEMESTER 2013-2014

EEE C434/EEE F343 Digital Signal Processing

Comprehensive Examination

Part—A (Closed Book)

Time-: 90 Min(Approximate)Max Mark-: 80 Date:December 10, 2013

Instruction:-Q.No 1-50 each carry ONEmark and 51-56 carryFIVEmarks.Write the correct answer with

penclearly only in the space provided. Use back of main answer book for rough work. Overwriting or

ambiguity will not be considered for recheck.

1. What is the clock cycle period of TMS320C6713 processor?

[A] 2.22 nsec [B] 4.44 nsec [C] 4.1 nsec [D] 8.12n nsec

2. Which of the following is a correct possible sampling rate for AIC23 codec?

[A] 22.1 KHz [B] 24.1 KHz [C] 44.1 KHz [D] 48.1 KHz

3. The TMS320C6713 processor can execute maximum _____ number of multiplicationsinstructions

simultaneously?

[A] 2 [B] 4 [C] 8 [D] 16

4. What is the maximum number of instructions that can be present in an execute pack?

[A] 2 [B] 4 [C] 8 [D] 16

5. The self test program that is used to test the DSK TMS320C6713 kit is present in_____.

[A] RAM [B] ROM [C]CPLD [D]Flash memory

6. Pick the odd man out

[A] [B] [C] [D]

7. To use MATLAB variables as Simulink block parameters, where do you need to define their values?

[A] Simulink library browser [B] Simulink model editor

[C] MATLAB current directory [D] MATLAB workspace

8. What are the possible ways to create a subsystem?

[A] Select blocks in a MATLAB window and group them into a subsystem.

[B]Select blocks in MATLAB command prompt and type “subsystem” in the command window.

[C]Drag a subsystem block into a model, and add blocks to the subsystem window.

[D]Drag variables from MATLAB workspace as a group into a Simulink model

9. Which among [A], [B], [C] and [D] is a correct match sequence?

(a) FDA tool [1] Signal Processing and technical visualization

(b) MATLAB [2] IDE for signal processing, micro controllers and ARM embedded processors

(c) Xilinx [3] A package for digital electronics for predefined system functions

A

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(d)Simulink [4] Modelling, simulating and analyzing non-linear simulations of dynamic systems

(e) CCS [5] It is a GUI used to modify the existing filter designs

[A] [2] (e) [4], (d) [3], (c) [1], (b) [5], (a)

[B] [2] (e) [5], (d) [3], (c) [1], (b) [4], (a)

[C] [1] (e) [4], (d) [3], (c) [2], (b) [5], (a)

[D] [2] (e) [4], (d) [3], (c) [5], (b) [1], (a)

10. TMS320C6713 is capable of performing:

[A] Only fixed-point operations [B] Only floating point operations [C] Both [D] None

11. Of the various support files in CCS, asm is used for

[A] Initialize the DSK and serial ports [B] header file with function prototypes

[C] sample linker command file [D] Interrupt handler

12. TMS in TMSC6713 stands for _____

[A] Texas Manufactured Semiconductors [B] Texas Mixed Signals

[C] Experimental Device [D] Qualified device

13. Which version of CCS we are using in our lab?

[A] CCS V 3.1 [B] CCS V 3.3 [C] CCS V 5.1 [D] CCS V 5.3

14. The cmd file included in simulation process in CCS _____

[A] Contains instructions [B] Maps memory locations for storing data, program

[C]Contain interrupt [D] All of above

15. The MATLAB command that outputs the number of rows and columns of a matrix [A]dimensions [B]mdim [C]msize [D] size

16. In FDAtool for filter design when we chose filter order as specify order, which of the following specification is not available for us to provide? [A]Fs [B]Fpass [C]Apass [D]Wpass

17. Using FDAtool, to which type of filter, a low pass filter cannot be transformed? [A]High pass filter [B] Multiband filter[C] High pass filter[D]LPF cab be transformed to all three.

18. Which among the following cannot be viewed using FDAtool for a filter? [A]Impulse response [B]step response [C] ramp response [D] None of these

19. Which of the following information cannot be obtained from Filter information tab in FDAtool? [A] Filter structure[B] Stability [C] Linear phase or not [D] All of these can be obtained

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20. For _____ filter the gain in stop band (for larger frequency) decreases by 6 dB by increasing the filter order by one. [A]Bessel [B]Chebyshev [C] Butterworth [D]Elliptical

21. The following is an impulse response of a

[A] FIR High-pass filter [B]FIR low pass Filter [C] IIR bandpass filter [D] FIR Band pass filter

22. Which of the following is a Chebyshev polynomial for N = 4. [A]8Ω4 -8Ω2+ +1 [B] 4Ω4 -4Ω2+ +1 [C] 4Ω4 -8Ω2+ +1 [D] 3Ω4 -3Ω2+ +1

23. A Chebyshev filter behaves as a _____ filter for zero ripple. [A]High pass [B] Low pass [C] Band pass [D] All pass

24. Which type of linear phase filter is not suitable for high pass filter? [A]Type 2 [B] Type 3 [C] Type 2 and 3 [D] Type 3 and 4

25. )160sin(2)40sin( tt and which of the following are identical after sampling at 100 Hz:

[A]0 [B] )40sin( t [C] )40sin(3 t [D] )160sin( t

26. What is the order of the Bandpass filter obtained from the frequency transformation of a low pass filter of order N. [A] N [B]N/2 [C]2N [D]2N-1

27. The inverse z-transform of 1

22 z

zis:

[A] ][2

sin2 nun

[B] ][)cos(2 nun [C] ][)sin(2 nun [D] n)1(

28. The z-transform of ][)4(][)2( nunu nn is:

[A]82

12 zz

[B]822

2

zz

zz [C]

822

2

2

zz

zz [D]

822

2

zz

zz

29. For an LTI system transfer function )2)(1(

)(

zz

zzH , the impulse response ][nh is:

[A] )()(2 nunun [B] ][][2 nunun [C] ][3][2 1 nunun [D] )(5)(2 nunun

30. For an LTI system transfer function )2)(1(

)(

zz

zzH , the response to ]1[][][ nnnx is:

[A] ]1[2 1 nun [B] ][2 nun [C] ]1[2 1 nun [D] ][][2 nunun

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31. In Fourier series method to get the transfer function of realizable filter, )(zH is to be multiplied by

[A] 2/)1( NZ [B] 2/)1( NZ [C] )1( NZ [D] )1( NZ

32. The abrupt truncation of Fourier series results in oscillation in [A] Pass band [B] Stop band [C] Both [D] None of these

33. The frequency response of a digital filter is [A]Periodic [B] Non periodic [C]Don't know [D] None of these

34. For Hamming window the width of the main lobe is [A] 2π/N [B] 4π/N [C] 8π/N [D] 12π/N

35. For Blackman window, the peak side lobe magnitude in dB is [A] -13 [B] -31 [C]-41 [D] -58

36. The non-linearity in the relationship between and is known as [A]Frequency mixing [B] Frequency warping [C] Unwarping [D] Aliasing

37. In the impulse invariant transformation, the relation between and is? [A] T [B] T/ [C] T [D] T/

38. Chose the appropriate statement for Bilinear transformation used for IIR filter design [A] non-linearity relationship between and [B] Can be used for low pass filter [C] Can be used for design of high pass filter [D] All the statements are valid

39. A LPF stop band frequency is 0-250Hz. The sampling frequency is 4KHz. Its analog prewraped frequency is___. Assume T = 2. [A]0.4142 [B] 0.1989 [C]0.1250 [D]0.0625

40. The down sampled signal is obtained by multiplying the sequence ][nx with

[A] impulse function [B] unit step function [C] train of impulse [D] unit sample function

41. Up sampling by a factor of I introduces [A] I zeros between samples [B] I-1 zeros between samples

[C] no zeros [D] I/2 zeros between samples

42. A delay of one sample period before up-sampling leads to a delay of how many samples periods after up

sampling by I

[A] I [B] I-1 [C] I/2 [D] 1

43. For which frequency 0 are the outputs ][nx of these two systems identical? In both systems, LPF is an

ideal LPF with cutoff frequency 3 .

System# 1: System# 2:

[A] 3.0 [B] 6.0 [C] 75.0 [D] C & B 44. Modified Havard architecture allow maximum_____ data memory access per cycle

[A] One [B] Two [C] Three [D] Four

45. What is the maximum and minimum unbiased exponent value of a single precision floating point number?

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[A]+ 127 and -127 [B] + 127 and -126 [C] + 126 and -127 [D] + 126 and -126

46. When we express +0.5 in single precision floating point format, its fraction part will be [A] 100000….0 [B]1111000…0 [C] 00000….0 [D]000000….1

47. When we express +0.5 in single precision floating point format, its exponent part will be [A] 00000000 [B]01111110 [C] 01000000 [D]00000001

48. Which DSP processors use only big endian format? [A] Motorola [B]Analog devices [C] Texas instrument [D]Lucent

49. Which of the following is not correct for RISC over CISC? [A] Simple instruction set [B] Less time to execute [C]Program are compact [D]Easy to pipeline

50. Which TI processor uses VLIW architecture [A] TMS320C54X [B] TMS320C55X [C]TMS320C4X [D] TMS320C67X

51. Determine the type of filters(LPF,HPF,BPF,BSF,APF) the following TF corresponds to: [5]

[A] 112

1 z

[B] 21214

1 zz [C] 213

2 z

[D] 6z [E] 1

1

1

1

z

z

52. (a) What is the decimal value of the following number represented in IEEE 754 single precision format?

2

00000000000000000000100100011100 [2.5]

(b) Quantize coefficient 0.121 using Q7 format (use rounding) and find out the error: [2.5]

53. Give the expression for a second order band pass IIR digital filter TF )(zH for the specification given as:

55.00 and 25.0BW [5]

54. A causal LTI FIR discrete-time system is characterized by an impulse response

]5[]4[]3[]2[]1[][][ 654321 nananananananh . For what value of

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impulse response samples (relationbetween 654321 ,,,,, aaaaaa ) will its frequency response )( jeH

have a constant group delay? [5]

55. A causal LTI discrete time system has an output y(n)= (0.4)nu(n)-0.3(0.4)

n-1u(n-1) for an input

x(n)= (0.2)nu(n). [5]

a) Write the transfer function of the system.

b) Sketch the direct form realization of the system.

56. Two finite duration sequences ][1 nh and ][2 nh of length 8 are related by a circular shift, i.e.;

821 ][ mnhnh . What is the relation between the magnitudes of their 8 point DFT's. [5]

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BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI

Pilani- Hyderabad-Goa campus

FIRST SEMESTER 2013-2014

EEE C415 : Digital Signal Processing

Comprehensive Examination

Part—B (Open Book)

Time-: 90 Min (Approximate) Max Mark-: 60 Date:10-12-2013

[1] (A) The system shown below in figure (a) performs sampling rate conversion by a factor of 3/4. Plot the spectrums with proper leveling for all pipeline points i.e.;

)(,)(,)(,)(,)( 321 YandVVVHD . The spectrum of input x(n) is given in figure (b).

Fig. (a) Fig. (b) [10]

(B) A signal )(tx is sampled with sampling frequency of 50 kHz to get )(nx . A decimator is used

to downsamples this signalx(n) by a factor D=5. The following specifications should be fulfilled by the filter used in decimeter: Passband: 0 - 4 kHz Passband ripple : 0.1 dB (i.e. between 0 dB and -0.1 dB) Transition zone : 4 - 5 kHz Stopbandattenuation : 30 dB Sketch the block diagram of the decimator and calculate the order of FIR equiripple filter that fulfills the specifications. [5]

[2] Design a FIR band-pass filter )(zH BP , using the Fourier series method and window approach (as

instructed below),for the following specifications:

Sampling rate : 10TF MHz

Edge Frequencies : 25.11 sF MHz, 875.11 pF MHz, 25.12 pF MHz, 2sF to be

determined

Minimum stop-band attenuation : 55s dB

(A) Find the appropriate window and the minimal filter length. (B) Obtain the formula of the filter impulse response with all frequency values inserted into the

formula.

(C) Determine an appropriate value for the stop-band edge frequency 2sF .

(D) Obtain the amount of peak ripple p (in dB) of )(zH BP in the pass-band? [5+3+2+5]

HINT: Window-based design uses identical bandwidths PTO.

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[3] (A) Design a Chebyshev type-1high-pass IIR filter using Bilineartransformation to fulfill the

specifications given in figure (c). The sampling frequency 8sF kHz. Assume T =1. [10]

HINT: Use the simplified Analog lowpassChebyshev Filter System Function

0

0

1)(

p

N

k

LP

s

k

sH where Nk ,,1

and

2

12

0

,

N1211

(B) If H(z) = 21

1

43

zz

z, Then find h(n) if ROC is 𝑧 > 1. [5]

[4] (A) A signal x(t) is sampled with 50KHz. The spectrum is given in figure(d). We need to

compress this signal using subband coding. Based on spectral analysis, it is decided to

split this spectrum into 5 subband signals of equal width. Then the signal with spectrum

in the middle band will be encoded with 16 bits. The signals in 2nd

and 4th

band will be

encoded with 8-bits and that in 1st and 5

th band with 4-bits. [3+3+1+1=8]

(a) Show the analysis system in the subband coding indicating the sampling rate at each point.

(b) Find the bitrate per second that will be obtained after subband coding.

(c) Find the bitrate per second that would have been obtained if we are not going for subband

coding and each sample is represented by 16bits.

(d) Find the compression ration that is obtained in (b) with respect to (c).

Fig (d)

(B)Give the structural realization of the following system with minimum number of multipliers:

H(z) =

2121

5

11

3

11 zzzz [7]

End

Fig. (c)