**MODEL QUESTION PAPER**

**B.E. Electronics and Instrumentation Engineering**

**V Semester**

**EI335 – DIGITAL SIGNAL PROCESSING**

Time : 3 Hours Max. Marks : 100 marks

# Answer all questions

** **

**PART – A **(10 x 2 = 20 marks)

PART-A 10 x 2 = 20 Marks

- Differentiate between analog and digital signal. Why Digital signal processing is widely used than analog signal processing.
- State Shannon’s Sampling theorem.
- Determine the Z-transform of (1/2)
^{n}[ u[n]-u[n-8]] and indicate its ROC. - Compare FIR and IIR filter.
- What are the advantages of linear phase characteristics? Which systems exhibit linear phase?
- Show that the system described by the difference equation is an all pass system

3 y(n) – y(n-1) = -x(n) + 3x(n-1)

- Mention few application areas where speech coding is required.
- Explain the circular addressing mode of DSP processor
- Find the DFT of the signal x(n)= {1,3,5,7}.
- Distinguish between recursive and non-recursive realizations of filters.

**PART-B** (5×16 = 80 Marks)

11.i) Show that Z-Transform of x*(n) is X*(z*). (4)

ii) Consider a linear shift-invariant discrete system with input x(n) and output y(n) for which

y(n-2) – 2.5 y(n-1) +y(n) =x(n)

By considering the pole-zero pattern associated with the difference equation, determine the three possible choices for the unit-sample response of the system. Comment on the stability of the system in each case. (12)

12.a)i) Find the DFT of the sequence {1,1,1,1,2,2,2,2} using radix-2 Decimation-in-Time FFT. Sketch the magnitude and phase plot. (12)

ii) What is the need for FFT? (4)

**(OR)**

12.b)i) Find the DFT of the sequence {1,1,1,1,2,2,2,2} using radix-2 Decimation-in-Frequency FFT. (12)

ii) Write about over lap save method. (4)

13.a) The specification of the desired low pass filter are:

A_{min }= 22 dB and A_{max }= 3 dB ω_{p} = 0.2П and ω_{s} = 0.4П

Design a Butterworth digital filter using Bilinear Transformation. (A_{min }and A_{max} are attenuation) (16)

**(OR)**

13.b) Design and also realize a high pass FIR filter with a cutoff frequency of 1.3 rad/sec and N=9. (16)

14.a)i) Perform the linear convolution of (1/4)^{n} u(n) and (1/2)^{n} u(n). (6)

ii) Is it possible to perform linear convolution through circular convolution. If so how?

(2)

iii) Find the Discrete Fourier Series of the following periodic sequence. (8)

**(OR)**

14.b)i) Explain about the Frequency Transformation that will be adopted in IIR filter design. (4)

ii) The specification of the desired low pass digital filter are

A_{min }= 12.4 dB and A_{max }= 0.915 dB ω_{p} = 0.25П and ω_{s} = -0.5П

Design a Chebyshev digital filter using impulse invariant transformation. (A_{min }and A_{max} are attenuation). (12)

15.ai) Highlight the special blocks of the Digital Signal Processor Architecture over the regular Micro-Controller based Architectures. (16)

**(OR)**

15.b)i) Explain how bit-reversal is achieved in the Texas based DSP Processor. (8)

ii) Show that FFT can be evaluated with lesser machine cycles using DSP processor compared to any of Micro-controller. (8)

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