Download AKTU B-Tech 6th Sem 2015-2016 NEC 011 Digital Signal Processing Question Paper

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NEC-011

(Following Paper ID and Roll No. to be filled in your Answer Books)

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Paper ID: 131661 Roll No.

B.TECH.

Theory Examination (Semester-VI) 2015-16

DIGITAL SIGNAL PROCESSING

Time: 3 Hours Max. Marks: 100

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Section-A

1. Attempt all parts. All parts carry equal marks. Write answer of each part in short.

   (2×10 = 20)

   1. What is Discrete Time Fourier Transform and How it is related to Discrete Fourier Transform?
   2. Establish the relation between Z-transform and DFT.

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   3. What is zero padding? What are its uses?
   4. Calculate number of multiplications needed in calculation of DFT and FFT of 32 point sequence and also calculate speed improvement factor.
   5. Explain Bit-reversal and In-place computation.
   6. Obtain Cascade realization with minimum number of multipliers.
   7. What is Spectral leakage? Give remedy to this problem.

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   8. What are the main disadvantages of designing IIR filters using windowing technique?

Section-B

Attempt any five questions from this section. (10×5=50)

2. 1. Prove that multiplication of the DFTs of two sequences is equivalent to the circular convolution of the two sequences in the time domain.

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   2. If the 10-point DFT of x(n) = d(n)-8(n-1) and h(n) = u(n)-u(n-10) are X(k) and H(k) respectively, find the sequence w(n) that corresponds to the 10-point inverse DFT of the product H(k).X(k).

   (7+8)

3. 1. (i) Compute 4-point DFT of the following sequence using linear transformation matrix

      x(n) = (1, 1, -2, -2)

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      (ii) Find IDFT x(n) from X(k) calculated in part(i).

      (2.5×2=05)

4. 1. Find the 10-point DFT of the following sequences:

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      1. x(n) = d(n)+d(n-5)
      2. x(n) = u(n)-u(n-6)
      3. x(n) = cos(?p/2)

   2. (i) Show that the same algorithm can be used to compute IDFT of X(k) calculated in part (a).

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   3. Compute the DFT of following 8-point sequence using 4-point Radix-2 DIT algorithm.

      x(n) = {2, 2, 2, 2, 1, 1, 1, 1}

   4. Obtain Direct Form I, Direct Form II and Parallel Form structures for the following filter

   y(h) = ³/₄y(n-1)+¹/₈y(n-2)+x(h)+³/₄x(n-1)+¹/₂x(h-2)

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   5. Realize the system with transfer function

      H(z) = (2+z^-1)(1+2z^-1)/(1-0.4z^-1)(1+0.7z^-1)

      1. Direct form
      2. A cascade of first-order and second-order system realized in transposed DF II
      3. A Parallel connection of first-order and second-order systems realized in DF II (2+4+4)

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   6. A filter is to be designed with the following desired frequency response:

      Ha(e^j?) = 0,                  |?|=p/4 \\ e^-j2?,         p/4=|?|=p

      Transform the prototype LPF with system function

      HP(S) = Op / (s+Op)

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      into a

5. Use Radix-2 DIT algorithm for efficient computation of 8-point DFT. (10)
6. 1. An FIR filter has following symmetry in the impulse response:

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   h(n) = h(M-1 –n) for M odd.

   Derive its frequency response and show that it has linear phase.

   2. Discuss the Bilinear Transformation method of converting analog IIR filter into digital IIR filter. What is Frequency Warping?

   (7+8)

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