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II Semester M.E. (Electronics and Communication) Degree Examination, January 2013 2K 9EL 214 : DSP ALGORITHMS AND ARCHITECTURE Time : 3 Hours

Max. Marks : 100

Answer any five full questions : 1. a) Explain sampling rate increase by an integer factor L using anti-imaging filter and derive input-output relationship in both time and frequency domains. 10 b) Find an output of decimator with decimation factor 3. Given filter coefficients h(n) = {0.03, 0.15, 0.31, 0.15, 0.03} and input x(n) = {1, 2, 3, 4, 1, 2, 1} using z-transform and verify the result using linear filtering. 10 2. a) Design a sampling rate converter to convert 8 KHz signal to 22 KHz signal. Derive an output expression in time and frequency domains. 10 b) What are Quadrature Mirror Filter banks ? Derive a condition for alias-free QMF bank.

10

3. a) Determine output of digital filter for given x(n) = δ (n) + δ (n – 1) + δ (n – 2) and h(n) = u(n) – u(n – 4) using i) Linear convolution and ii) Circular convolution.

10

b) Find IFFT using DIT algorithm for X(K) = {4, (1 – j2.4), 0, (1 – j0.4), 0, (1 + j0.4), 0, (1 + j2.4)}.

10

4. a) Define mother wavelet and discuss the properties of wavelet transforms.

10

b) Explain adaptive filtering and discuss LMS and RLS adaptive algorithms.

10

5. a) Design a digital low pass FIR filter of length 7 with cutoff frequency 500 Hz and sampling rate of 2 KHz using Hamming window. b) Design FIR differentiator for H(ejw) = jw, for − π ≤ w ≤ π using rectangular window with w = 7.

10 10

P.T.O.

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6. a) Design Chebyshev digital filter using Bilinear transformation for the specifications 1 2

≤ H( w ) ≤ 1, H(w ) ≤ 0 .1,

0 ≤ w ≤ 0 .2 π 0 .5 π ≤ w ≤ π

.

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b) Design digital filter using impulse invariance method with T = 1 sec. for H ( S) =

2 . S + 8S + 15 2

7. a) Discuss addressing modes of a DSP processor with examples.

10 10

b) Describe with examples sampling period reduction and parallel processing in applications of unfolding. 10 8. a) Describe with an example any one shortest path algorithms.

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b) Describe with examples longest path matrix algorithm and any one algorithm for computing iteration bound. 10 _______________________