STUPIDSID
Answer the following
1 (a) i)
Check whether the following signal is periodic or not. If a signal is
periodic, find its fundamental period.
\[X[n]=\cos^{2}\left ( \dfrac{\pi}{8} \right )8\]
\[X[n]=\cos^{2}\left ( \dfrac{\pi}{8} \right )8\]
2 M
1 (a) ii)
X (n) = (-0.5)n u (n). State whether it is energy or power signal. Justify
2 M
1 (a) iii)
Define and explain the convolution and correlation.
2 M
1 (a) iv)
Determine if the following system describe by,
Y(t) = Sin [ x (t+2) ] ; is memory less, causal ,linear ,time invariant, stable.
Y(t) = Sin [ x (t+2) ] ; is memory less, causal ,linear ,time invariant, stable.
2 M
Answer the following
1 (b) i)
Compute the convolution y(n) = x(n) * h(n), Where
\[X (n) = \{1, 1,\underset {\uparrow }{0}, 1, 1\} \ and \ h(n) = \{1, \underset {\uparrow }{-2}, -3, 4\} \]
\[X (n) = \{1, 1,\underset {\uparrow }{0}, 1, 1\} \ and \ h(n) = \{1, \underset {\uparrow }{-2}, -3, 4\} \]
3 M
1 (b) ii)
Determine if the systems described by following equations are causal or
non causal and stable or not.
(1) T[x(n)] = ex(n)
(2) Y(n) = x(2n)
(3) Y(n) = x(n2 ).
(1) T[x(n)] = ex(n)
(2) Y(n) = x(2n)
(3) Y(n) = x(n2 ).
3 M
2 (a)
State and prove the properties of Z- transform
(i) Convolution of two sequence.
(ii) Differentiation in Z domain.
(i) Convolution of two sequence.
(ii) Differentiation in Z domain.
7 M
2 (b)
Given the two sequence of the length 4 are:
X(n) = {0, 1, 2, 3} h(n) = {2, 1, 1, 2}
Find the circular convolution.
X(n) = {0, 1, 2, 3} h(n) = {2, 1, 1, 2}
Find the circular convolution.
7 M
2 (c)
Using graphical method, obtain a 5- point circular convolution of two DT signals defined as,
X(n) = (1.5)n , 2 ≥ n≥ 0
Y(n) = 2n-3, 3 ≥ n ≥ 0.
X(n) = (1.5)n , 2 ≥ n≥ 0
Y(n) = 2n-3, 3 ≥ n ≥ 0.
7 M
3 (a)
Find Z transform and ROC of the following sequence.
(i) X1 (n) = [ 3[2n ] - 4 [3n ] ] u[n]
(ii) \[X_{2} (n) = [ (0.5)^{n}\sin\dfrac{\pi n}{4}]u(n)\]
(iii) X3(n)=n2-2n+3 for n≥0.
(i) X1 (n) = [ 3[2n ] - 4 [3n ] ] u[n]
(ii) \[X_{2} (n) = [ (0.5)^{n}\sin\dfrac{\pi n}{4}]u(n)\]
(iii) X3(n)=n2-2n+3 for n≥0.
7 M
3 (b)
State and prove the properties of DFT (I) Periodicity (II) Time shifting.
7 M
3 (c)
Determine the response of the system, \[Y(n)=\dfrac{5}{6}y(n-1)-\dfrac{1}{6}y(n-2)+x(n)\] to the input signals.
\[X(n)=\delta (n)-\dfrac{1}{3}\delta(n-1)\]
\[X(n)=\delta (n)-\dfrac{1}{3}\delta(n-1)\]
7 M
3 (d)
State and prove the properties of DFT
(I) Circular convolution (II) Multiplication of two sequences
(I) Circular convolution (II) Multiplication of two sequences
7 M
4 (a)
The transfer function of discrete time causal system is given below
\[H(z)=\dfrac{1-z^{-1}}{1-0.2z^{-1}+0.15z^{-2}}\]
Find the difference equation and draw cascade and parallel realization.
\[H(z)=\dfrac{1-z^{-1}}{1-0.2z^{-1}+0.15z^{-2}}\]
Find the difference equation and draw cascade and parallel realization.
7 M
4 (b)
Derive DIT FFT flow graph for N = 4 hence find DFT of
x(n) = {1, 2, 3, 4}
x(n) = {1, 2, 3, 4}
7 M
4 (c)
Consider discrete time linear causal system defined by difference equation.
\[y(n)-\dfrac{3}{4}y(n-1)+\dfrac{1}{8}y(n-2)=x(n)+\dfrac{1}{3}x(n-1)\]
Obtain cascade realization of the same.
\[y(n)-\dfrac{3}{4}y(n-1)+\dfrac{1}{8}y(n-2)=x(n)+\dfrac{1}{3}x(n-1)\]
Obtain cascade realization of the same.
7 M
4 (d)
Determine Inverse Z-transform of the following :
\[X(z)=\dfrac{3z^{-3}}{\left ( 1-\dfrac{1}{4}z-1 \right )^{2}}\] x(n) left handed system.
\[X(z)=\dfrac{3z^{-3}}{\left ( 1-\dfrac{1}{4}z-1 \right )^{2}}\] x(n) left handed system.
7 M
5 (a)
Compute the eight point DFT of a sequence
\[X(n)=\left ( \dfrac{1}{2},\dfrac{1}{2},\dfrac{1}{2},\dfrac{1}{2} ,0,0,0,0\right )\]
Using decimation in time FFT algorithm.
\[X(n)=\left ( \dfrac{1}{2},\dfrac{1}{2},\dfrac{1}{2},\dfrac{1}{2} ,0,0,0,0\right )\]
Using decimation in time FFT algorithm.
7 M
5 (b)
Write short note on multiplier-accumulator (MAC) hardware of DSP processor
7 M
5 (c)
Determine the response [y(n)] of FIR filter. Input x(n) is (1,2,2,1) and
h(n) is (1,2,3). Use DFT and IDFT formula.
7 M
5 (d)
Write short notes on:
1. Harvard architecture of DSP processor.
2. Hanning Window and Kaiser Window Functions
1. Harvard architecture of DSP processor.
2. Hanning Window and Kaiser Window Functions
7 M
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