Rr410201 Digital Signal Processing

RR

Code No: RR410201

IV B.Tech I Semester(RR) Supplementary Examinations, December 2009 DIGITAL SIGNAL PROCESSING (Electrical & Electronics Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Consider a LSI system with unit sample response h(n)n = αn u(n) where α is real and 0 < α < 1 . If the input is x(n) = β n u(n), 0 < |β| < 1 ,determine the the output f(n) in the form y(n) = (k1 αn + k2 β n u(n) by explicitly evaluating the convolution sum. (b) Define causality and stability of LSI system and state the conditions for stability. [12+4] 2. (a) Show that the frequency response of a discrete system is a periodic function of frequency. (b) Obtain the frequency response of the first order system with difference equation y(0) = x(n)+10y(n1) with initial condition y(-1) = 0 and sketch it comment about its stability. (c) State and prove the frequency shifting property of Fourier transform. [5+6+5] 3. (a) What is “ padding with Zeros ” with an example, Explain the effect of padding a sequence of length N with L Zeros or frequency resolution. (b) Compute the DFT of the three point sequence x(n) = {2, 1, 2}. Using the same sequence, compute the 6 point DFT and compare the two DFTs. [8+8] 4. (a) Implement the Decimation in frequency FFT algorithm of N-point DFT where N-8. Also explain the steps involved in this algorithm. (b) Compute the FFT for the sequence x(n) = { 1, 1, 1, 1, 1, 1, 1, 1 }

[8+8]

5. (a) Explain how the analysis of discrete time invariant system can be obtained using convolution properties of Z transform. (b) Determine the impulse response of the system described by the difference equation y(n)-3y(n-1)4y(n-2)=x(n)+2x(n-1) using Z transform. [8+8] 6. (a) Design a digital filter that will pass a 1 Hz signal with attenuation less than 2 db and suppress 4 Hz signal down to at least 42 db from the magnitude of the 1 Hz signal. (b) What are the limitations of Impulse invariance method?

[12+4]

7. Design a(low pass Finite Impulse Response filter that approximate the following frequency response: 1 ; 0 ≤ f ≤ 1000 Hz H(f ) = 0 ; elsewhere in the range 0 ≤ f ≤ fs /2 when the sampling frequency is 8000 sps. The impulse response duration is to be limited to 2.5 msec. Draw the filter structure. [16] 8. (a) Obtain the cascade and parallel form realisation of the LTI system governed by the equation. (b) Compare cascade and performance of direct and canonic forms. ?????

[12+4]