STUPIDSID
1 (a)
State the condition for stability of LTI system, determine the range of values of a and b for which the impulse time - invariant system with following given impulse response is stable. \[ h(n)= \left\{\begin{matrix}
a^n &m\le 0 \\ b^n
& n<0
\end{matrix}\right. \]
5 M
1 (b)
Find the Energy of the signal x(n)=0.5n u(n)+8nu(-n-1).
5 M
1 (c)
Find the values of x(n)= cos (0.25 π n) for n=0, 1, 2, 3. Compute the DFT of x(n) using FFT flow graph.
5 M
1 (d)
Find the cross correlation of the sequence \( x(n)= \big \{ \underset{\uparrow}{1} , 2, 3, 4 \big \} \text{ and }h(n)= \big \{ \underset{\uparrow}{2}, 4, 6 \big \}. \)
5 M
2 (a)
Determine whether or not the following signals are periodic If periodic specify its fundamental period.
(i) x1(n)= cos (0.5 π n + 0.3)
(ii) x2(n) = cos (0.3 πn) + 10 sin (0.25 π n).
(i) x1(n)= cos (0.5 π n + 0.3)
(ii) x2(n) = cos (0.3 πn) + 10 sin (0.25 π n).
10 M
2 (b)
Compute Linear convolution of causal x(n) and h(n) using overlap and method in time domain.
x(n)={1, 2, 3, 4, 5, 6, 7, 8}, h(n)={1, 1, 1}
x(n)={1, 2, 3, 4, 5, 6, 7, 8}, h(n)={1, 1, 1}
10 M
3 (a)
Check whether the given system y(n) = x(2n) - x(n-1) is:
i) Static or Dynamic
ii) Linear or non-linear
iii) Shift invariant or variant
iv) Causal or non causal.
v) Stable or unstable.
i) Static or Dynamic
ii) Linear or non-linear
iii) Shift invariant or variant
iv) Causal or non causal.
v) Stable or unstable.
10 M
3 (b)
State the following DFT properties:
i) Linearity property
ii) Periodicity
iii) Time shift
iv) Convolution
v) Time Reversal
i) Linearity property
ii) Periodicity
iii) Time shift
iv) Convolution
v) Time Reversal
10 M
4 (a)
For the causal LTI digital filter with impulse response given by h(n)=0.3 δ(n) - δ(n+1) + 0.38 δ(n-3) sketch the magnitude spectrum of the filter. Using DFT.
10 M
4 (b)
Let X (K) = {20, 0, -4+4j, 0, -4} is the 8 point DFT of a real valued sequence x(n)
i) Find X(K) for K=5, 6, 7.
ii) Find the 8 point DFT P(K) such that p(n) = (-1)n x(n) Using DFT property.
i) Find X(K) for K=5, 6, 7.
ii) Find the 8 point DFT P(K) such that p(n) = (-1)n x(n) Using DFT property.
10 M
5 (a)
Find circular convolution and linear using circular convolution for the following sequence x1(n) = {1, 2, 3, 4} and x2(n) = {1, 2, 1, 2}. Using Time Domain formula method.
10 M
5 (b)
Derive radix 2 DITFET flow graph and find the DFT of the sequence x(n) = {0, 1, 2, 3}
10 M
6 (a)
Write a detailed note on DSP Processor.
10 M
6 (b)
Write a detailed note on Carl's Correlation Coefficient Algorithm. Justify the necessary of Algorithm by given suitable example.
10 M
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