SPPU Digital Signal Processing - June 2014 Exam Question Paper

SPPU Electronics and Telecom Engineering (Semester 5)
Digital Signal Processing
June 2014

Total marks: --
Total time: --

INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

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)

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)=aⁿ u(n), h(n)=bⁿ 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{↑}{2}, 1, - 1}

$h(n)= \{1, \underset{\uparrow}{2}, 1, -1 \}$ Determine the response of the system to the input signal

x (n) = {\underset{↑}{1}, 2, 3, 1}

$x(n)= \{ \underset{\uparrow}{1}, 2,3,1\}$

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

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) = -aⁿ u(-n-1)
ii) x(n) = aⁿ u(n)+ bⁿ u (-n-1)

8 M

4 (a) A linear time invariant system is characterized by the system function

H (z) = \frac{3 - 4 z^{- 1}}{1 - 3.5 z^{1} + 1.5 z^{- 2}}

$H(z) = \dfrac {3-4 z^{-1}} {1-3.5z^1 + 1.5 z^{-2}}$ 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

8 M

4 (b) Determine the inverse z transform the following signals.

i) H (z) = \frac{1}{1 - 1.5 z^{- 1} + 0.5 z^{- 2}} R O C : | z | > 1 i i) X (z) = \frac{1}{(1 - z^{- 1}) (1 - z^{- 1})^{2}} f o r t h e c a u s a l s i g n a l

$i) \ \ H(z) = \dfrac {1}{1-1.5 z^{-1} + 0.5 z^{-2}} \ \ ROC: |z|>1 \\ ii) X(z)= \dfrac {1}{(1-z^{-1})(1-z^{-1})^2} \ for \ the \ causal \ signal$

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}

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{aligned} x (n) & = A & f o r 0 < n < L - 1 \\ = 0 & o t h e r w i s e \end{aligned}

$\begin {align*} x(n)&=A & for \ 0 < n<L-1 \\ &=0 & otherwise \ \ \ \ \ \ \ \ \end{align*}$

8 M

6 (b) Compute the eight point DIT-FFT of the following sequence

x (n) = {\begin{matrix} 1 & 0 < n <= 7 \\ 0 & o t h e r w i s e \end{matrix}

$x(n) = \left\{\begin{matrix} 1 &0< n <=7 \\0 & otherwise \ \ \end{matrix}\right.$

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

h (n) = \frac{1}{N} [\sum_{k = 1}^{\frac{N}{2}} 2 | H (k) | \cos [2 π k (n - a) / N] + H (0)]

$\displaystyle h(n)= \dfrac {1}{N} \left [ \sum^{\frac {N}{2}}_{k=1} 2 \big \vert H(k)\big \vert \cos [2 \pi k (n-a)/N]+ H(0) \right ]$ 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) = \frac{1}{1 + s / Ω_{c}}

$H_a(S) = \dfrac {1} {1+s/\Omega_c}$

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.

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

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

8 M

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