# Digital Signal Processing 2006-07

Note : Answer all the five questions.

1. Answer any four of the following :

(a) Explain briefly the basic elements of Digital 5 Signal Processing system.

(b) Explain the difference between multichannel 5 and multidimensional signals.

(c) What do you understand by Nyquist rate of 5 sampling ? Consider the analog signal xa (t) = 3 cos 50711 +10 sin3007if – cosIOOtc . What is Nyquist rate for this signal.

(d) What do you understand by power signal 5 and energy signal ? Determine the power

and energy of the unit step sequence.

(e) Briefly discuss the recursive and nonrecursive 5 realization of an FIR system moving average system.

(f) What are the different properties of the Z-transform ? Determine the Z-transform of the following signal using appropriate properties of Z-transform. x(n) = n anu(n)

2. Answer any four of the following :

(a) What are the necessary and sufficient 5 conditions that a frequency response

characteristic H(w) must satisfy in order for the resulting filter to be causal ?

(b)    What do you understand by the following : 5

(i) Passband ripple

(ii) Stopband ripple

(iii) Passband edge ripple and

(iv) Stopband edge ripple, with reference to a frequency selective filters ?

(c) What do you understand by Antisymmetric 5 FIR filters ?

(d) Briefly explain “Alternative theorem”. What is 5 the application of this theorem in the FIR filter design ?

(e) What are the four different cases that result 5 in a linear-phase FIR filters. Explain briefly any one out of the four case linear-phase FIR filters.

(f) What do you understand by (i) FIR differentiators and (ii) Hilbert transformers ? Explain in brief.

3. Answer any two parts of the following :

(a) Design a first-order digital low-pass filter 10 with a 3-dB cut-off frequency of wc =0.25% by applying the Bilinear transformation to the analog Butterworth filter Ha (s) = – 1 + -L

(b) What do you understand by Pade 10 approximation method to design an HR filter ? In what respect is this method different from method of frequency transformation ?

(c) Explain the impulse invariance method to 10 design an HR filter from an analog prototype. Show that the resulting mapping between the s-plane and the z-plane is not one-to-one.

4. Answer any two of the following :

(a) What do you understand by “sample rate conversion” and “multirate” digital signal processing systems ? Briefly describe two general methods of sampling rate conversions. Describe their advantages and disadvantages also.

(b)   Explain how parametric methods of power 10 spectrum estimation are different from nonparametric methods of power spectrum estimation ?

(c) Why autoregressive (AR) model is widely 10 used in parametric spectrum estimation ? How AR model is different from moving average (MA) model of parametric spectrum estimation ?

5.  Answer any two of the following :

(a) Draw the general block diagram of a modern 10 large radar system. Explain briefly the working of each block. Where, in this system block diagram, DSP hardware / software can be applied ?

(b) What do you understand by “channelvocoder” 10 for analog speech bandwidth compression system ? Suggest its digital implementation with the help of a block diagram. Briefly explain each of the blocks in the resulting block diagram.

(c) What are different signal processing functions 10 a DSP based radar system is expected to perform. Explain all the functions in brief.