**Anna University V Semester B.E. **

**Electronics And Communication Engineering**

**Digital Signal Processing**

**Time: 3hrs **

**Max Marks: 100**

**Answer all Questions**

**PART – A (10 x 2 = 20 Marks)**

1. What is the system impulse response if the input and output are x(n)=(1/2)_{}^{n} u(n), y(n)=(1/2)_{}^{n} u(n) respectively?

2. Determine the circular convolution of the sequence x_{1} (n)={1,2,3,1}, x_{2 }(n)={4,3,2,2}

3. What are the advantages and disadvantages of FIR over IIR filter?

4. Convert the non-recursive system H(z)=1+z^{-1}+z^{ –2}+^{ }z^{-3 }+z^{ –4 }into recursive system.

5. How are the limit cycle oscillations due to overflow minimized?

6. Determine the direct form realizations for the filter h (n)={1,2,3,4,3,2,1}

7. What is the effect of product Quantization due to finite word length?

8. What are the advantages of multistage implementation in multirate signal processing?

9. Define periodogram? How can it be smoothed?

10. Where will you place zero & poles in a filter to eliminate 50 Hz frequency in a sampled signal at sampling frequency F=600Hz?

PART – B (5 x 16 = 80 Marks)

11. Using FFT algorithm compute the output of linear filter described by h (n)={1,2,3,2,1} and input x (n)={1,1,1,1}

12.a) Design a Chebyshev digital low pass filter with the following specifications. pass band ripple ? 1 dB, pass band edge = 4Khz,stop band attenuation ? 40 dB, stop band edge = 6Khz & sampling rate = 24Khz. Use bilinear transformation.

**(OR)**

** **

12.b) Design a Butterworth IIR filter with the following specifications

0.8 ? |H (e^{jw})| ? 1 0 ? ? ? 0.2p

|H (e^{jw})| ? 0.2 0.6 p ? ? ? p

Use Impulse Invariant method.

13.a) Design an FIR linear phase digital filter approximating the ideal frequency response,

H_{d} (?) = 1, 0 ? | ?| ? p/6

0, p/6<| ?| ? p

Determine the coefficients of a 13-tap filter based on window method. Use hamming window.

** **

**(OR)**

** **

13.b) Design an FIR digital filter whose frequency spectral samples are

H (k) = e^{-j16}^{pk/17 }0 ? k ? 4

= 0 5 ? k ? 12

= e^{-j16}^{p(k-17)/17 }13 ? k ? 16

Use Hanning window.

14.a) Consider the system y(n) = 0.8575 y(n-1) – 0.125 y(n-2) + x(n)

i) Compute the poles & Design the cascade realizations of the system.

ii) Quantize the coefficients of the system using truncation, maintains a sign bit plus three other bits. Determine the poles of the resulting system.

iii) Determine the resulting frequency at –3dB. Assume sampling frequency as F_{s}= 1000Hz.

**(OR)**

** **

14.b) The transfer function for an FIR filter is given by H(z)=1-1.334335z^{-1}+ 0.9025z^{-1} Draw the realization diagram for each of the following cases. (i) Transversal structures (ii) a two-stage lattice structure. Calculate the values of the coefficients for the lattice structure

15.a) Consider the signal x (n)=a^{n}u (n), |a|<1.Determine the spectrum X(w).The signal x(n) is applied to a decimator that reduces the rate by a factor of 2. Determine the output spectrum. Discuss the design criteria for anti-aliasing filter.

**(OR)**

** **

15.b) Determine the Power Spectral density estimate of the signal x(n)=(0.9)^{n},0£n£20 using Blackman-Tukey method.