Answer any one question from Q1 and Q2

1 (a)
State any four advantages of Digital Signal Processing over Analog Signal Processing.

4 M

1 (b)
Obtain the direct form I, direct form II realization of the following system.

y(n) - 0.2y(n-1) + 0.3y( n-2)= x(n)+3.6x(n-1)+0.6x(n-2)

y(n) - 0.2y(n-1) + 0.3y( n-2)= x(n)+3.6x(n-1)+0.6x(n-2)

8 M

1 (c)
Determine the impulse response h(n) for the system described by the second-order difference equation y(n) - 3y(n-1) - 4 y(n-2) = x(n) + 2x(n-1)

6 M

2 (a)
Perform the convolution on the following sequence

i) x(n) = { 3 2 4 1) , h(n) = ( 1 2 1 2)

ii) x(n)=a

i) x(n) = { 3 2 4 1) , h(n) = ( 1 2 1 2)

ii) x(n)=a

^{n}u(n), h(n)=b^{n}u(n) if a=b
8 M

2 (b)
Comment on stability of Linear Time ?Invariant systems.

6 M

2 (c)
The impulse response of LTI system is \[
h(n)= \{1, \underset{\uparrow}{2}, 1, -1 \} \] Determine the response of the system to the input signal \[ x(n)= \{ \underset{\uparrow}{1}, 2,3,1\} \]

4 M

Answer any one question from Q3 and Q4

3 (a)
State and prove the following properties of Z transform

i) Convolution of two sequences

ii) Differentiation in Z domain

i) Convolution of two sequences

ii) Differentiation in Z domain

6 M

3 (b)
State and prove relationship between z transform and DFT.

2 M

3 (c)
Determine the Z transform and sketch the ROC of the following signals.

i) x(n) = -a

ii) x(n) = a

i) x(n) = -a

^{n}u(-n-1)ii) x(n) = a

^{n}u(n)+ b^{n}u (-n-1)
8 M

4 (a)
A linear time invariant system is characterized by the system function \[ H(z) = \dfrac {3-4 z^{-1}} {1-3.5z^1 + 1.5 z^{-2}} \] Specify the ROC OF H(z) and determine h(n) for the following conditions:

i)The system is stable

ii) The system is causal

iii)The system is anticausal

i)The system is stable

ii) The system is causal

iii)The system is anticausal

8 M

4 (b)
Determine the inverse z transform the following signals. \[
i) \ \ H(z) = \dfrac {1}{1-1.5 z^{-1} + 0.5 z^{-2}} \ \ ROC: |z|>1 \\ ii) X(z)= \dfrac {1}{(1-z^{-1})(1-z^{-1})^2} \ for \ the \ causal \ signal \]

8 M

Answer any one question from Q5 and Q6

5 (a)
State and prove any four properties of DFT.

8 M

5 (b)
Perform the circular convolution of the following sequences

x1(n) = {1, 2, 3, 4} x2(n) = {2, 1, 2, 1}

x1(n) = {1, 2, 3, 4} x2(n) = {2, 1, 2, 1}

4 M

5 (c)
Compute four point DFT of the following sequence x (n) ={ 1, 2 , 3, 4 }

4 M

6 (a)
Find the DTFT of the following sequence of length L. \[\begin {align*} x(n)&=A & for \ 0 < n<L-1 \\ &=0 & otherwise \ \ \ \ \ \ \ \ \end{align*} \]

8 M

6 (b)
Compute the eight point DIT-FFT of the following sequence \[ x(n) = \left\{\begin{matrix}
1 &0< n <=7 \\0
& otherwise \ \
\end{matrix}\right. \]

8 M

Answer any one question from Q7 and Q8

7 (a)
Use frequency sampling method to design a lowpass filter to meet the following specifications. N = 9. Sampling frequency = 18000 samples/sec. Passband = 0-5 KHz

10 M

7 (b)
Show that the impulse response coefficients of a linear phase FIR filter with positive symmetry, for N even, is given by \[ \displaystyle h(n)= \dfrac {1}{N} \left [ \sum^{\frac {N}{2}}_{k=1} 2 \big \vert H(k)\big \vert \cos [2 \pi k (n-a)/N]+ H(0) \right ] \] where α=(N-1)/2 and H(k) are the samples of the frequency response of the filter taken in the frequency range of (0 - 2π).

8 M

8 (a)
Design a digital low pass filter with a 3db cutoff frequency of ωc =0.2π by applying the bilinear transformation to the analog Butterworth filter \[ H_a(S) = \dfrac {1} {1+s/\Omega_c} \]

4 M

8 (b)
Show that the bilinear transformation maps jω-axis in the s-plane onto unit circle in z- plane, and maps the left half s-plane inside the unit circle in z-plane.

4 M

8 (c)
Design a digital low-pass filter to meet the following specifications.

Passband cutoff frequency = π/2

Minimum passband gain= 0.9

Maximum stopband gain= 0.2

Use Butterworth approximation and Bilinear transformation.

Passband cutoff frequency = π/2

Minimum passband gain= 0.9

Maximum stopband gain= 0.2

Use Butterworth approximation and Bilinear transformation.

10 M

Answer any one question from Q9 and Q10

9 (a)
Explain sampling rate conversion by a non-integer factor.

8 M

9 (b)
What is the need of antialiasing filter prior to down sampling and anti-imaging filter after up sampling a signal?

8 M

10 (a)
What is the need of polyphase interpolation? Explain in detail polyphase interpolator.

8 M

10 (b)
Explain application of DAC in compact disc Hi-Fi systems.

8 M

Answer any one question from Q11 and Q12

11 (a)
Explain the desirable architectural features for selecting a digital signal processor.

8 M

11 (b)
Write short note on

i) Pipelining

ii) MAC Unit

i) Pipelining

ii) MAC Unit

8 M

12 (a)
Explain five important salient features of TMS 320C6713 digital signal processor and draw its functional block diagram.

8 M

12 (b)
Write short note on

i) Harvard Architecture

ii) Barrel Shifter

i) Harvard Architecture

ii) Barrel Shifter

8 M

More question papers from Digital Signal Processing