STUPIDSID
1(a)
State and prove the relationship between z-transform and DFT.
6 M
1(b)
Determine N point DFT of \[x(n)=cos\frac{2\pi K_{0}n}{N},0\leq K\leq N-1\]
6 M
1(c)
Find the IDFT of x(k) = {255, 48.63 + j166.05,-51+j102, -78.63+j46.05, -85, -78.63-j46.05,-51-j102, 48.63-166j}.
8 M
2(a)
State and prove the relationship between z-t and prove the following properties :
i) Symmetry property
ii) Parseval's theorem
i) Symmetry property
ii) Parseval's theorem
8 M
2(b)
Prove :i) Symmetry and ii) Periodicity property of a twiddle factor.
8 M
2(c)
Find the output y(n) of a filter whose impulse response is h (n) -{1,2,3,4} and the input signal to the filter is x(n) - {1,2,1,-1,3,0,5,6,2,-2,-5,6,7,1,2,0,1} using overlap add method [Use 6 point circular convolution.]
8 M
3(a)
Determine y(n)\[x_{1}\circledast x_{2}(n),-n+1,0\leq n\leq 5\ and \ x_{2}(n)=cos\pi0\ n\leqn\leq 5 \] Using stockhalm's method.
10 M
3(b)
Develop DIT FFT algorithm and write signal flow graph for N=8.
8 M
3(c)
Explain in-place computation of FET.
2 M
4(a)
Explain bit reversal property used in FFT algorithm for N = 16
3 M
4(b)
Develop DIT - FFT algorithm for N = 9.
7 M
4(c)
Find IDFT of x(k) -{36,-4+j9.7,-4+j4,-4+j1.7,-4,-4-j1.7,-4-j4,-4-j9.7}. Using DIF FFT algorithm.Show clearly all the intermediate results.
10 M
5(a)
Design a Chebyshev filter to meet the following specifications :
i) Pass band ripple \[\leq \] db
ii) Stop band attenuation \[\geq \] 20 db
iii) Pass band edge : 1 rad/sec
iv) stop band edge : 1;3 rad/sec
i) Pass band ripple \[\leq \] db
ii) Stop band attenuation \[\geq \] 20 db
iii) Pass band edge : 1 rad/sec
iv) stop band edge : 1;3 rad/sec
10 M
5(b)
Distinguish between IIR and FIR filters.
4 M
5(c)
Derive an expression for order of a a low pass Butterworth filter.
6 M
6(a)
Realize FIR linear phase filter for N to be even.
8 M
6(b)
Evaluate the impulse response for input x(n) \[^{-}\delta (n)\] of three stage lattice structure having coefficients \[K_{1}=0.65,K_{2}=-0.34\ and \ K_{3}- 0.8.\] Also draw its direct form - I structure.
12 M
7(a)
Explain how an analog filter is mapped on to digital filter using impulse invariance method. What are the limitations of the method?
10 M
7(b)
Obtain direct form - I and lattices structure for the system described by the difference equation[y(n)=x(n)+frac{2}{5} imes(n-2)+frac{1}{3}x(n-3).]
10 M
8(a)
for the desired frequency response
\[H(\omega )=\left\{\begin{matrix} e^{j3\omega } -\frac{3\pi }{4}& < \omega < \frac{3\pi }{4}\\0,&\frac{3\pi }{4} < |\omega |< \pi \\ & \end{matrix}\right.\]
Find H(\omega\] for N = 7 using Hanning window.
\[H(\omega )=\left\{\begin{matrix} e^{j3\omega } -\frac{3\pi }{4}& < \omega < \frac{3\pi }{4}\\0,&\frac{3\pi }{4} < |\omega |< \pi \\ & \end{matrix}\right.\]
Find H(\omega\] for N = 7 using Hanning window.
10 M
8(b)
Show that for \[\beta |]- 0,Kaiser window becomes a rectangular window.
5 M
8(c)
Mention few advantages and disadvantages of windowing technique.
5 M
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