STUPIDSID
Answer the following (Any Four):
1 (a)
State and prove the convolution property of z-transform.
5 M
1 (b)
Draw the single butterfly of 2-Radix DIT & DIF FFT algorithm.
5 M
1 (c)
State and prove the complex conjugate property of DFT.
5 M
1 (d)
The transfer function of analog filter is \( H(S) = \dfrac {S+2}{(S+1)(S+3)} \) design a digital IIR filters by means of IIT. Assume T=0.1 Sec.
5 M
1 (e)
Determine IDFT of x(k)=[6, -1, -j, 0, -1+j] by using DIT FFT algorithm.
5 M
2 (a)
If x1(n)=[1, 2, 0, 3] and x(n)=[1, 2, 3, 2]. Find the DFT of both the sequence by using DFT only once (not otherwise).
10 M
2 (b)
Derive and draw the FFT for N=6=2.3 using DIT FFT algorithm.
10 M
3 (a)
If x1(n)=[1, 2, 3, 5] and x2(n)=[2, 4, 2, 3]. Obtain x1(n) ⊗ x2(n) by using DIF FFT algorithm.
10 M
3 (b)
Prove the relation between the analog and digital filter by means of Bilinear Transformation Technique.
10 M
4 (a)
Determine the output of a Linear FIR Filter whose impulse response h(n)={3, 2, 1} x(n)={1, 0, 2, 1, 0, -2, -1, 0, 3, 1} using over lap add method.
10 M
4 (b)
Determine the frequency response of the system h(n)=anu(n) magnitude and phase response of it.
10 M
5 (a)
\( y(n)=x (n) + \dfrac {1}{4} x (n-1) + \dfrac {1}{6} y (n-1)+ \dfrac {1}{6}y(n-z) \) Realize the system by using Direct form-I cascade and parallel form realization.
10 M
5 (b)
Design a digital Butterworth filter that satisfy the following constraint using Bilinear Transformation. Assume T=1 Sec \[ \begin {align*}
0.9= \le &|H(e^{j\omega})| \le 1 &0\le \omega \le \% \ \ \ \ \ &|H(e^{j\omega})| \le 0.2 & 3\pi/4 \le \omega \le \pi \end{align*} \]
10 M
6 (a)
A pass filter is to be designed which following frequency response \[ \begin {align*}
Hd(e^{j\omega}) =e^{-j3\omega} -&\dfrac {3\pi}{4} \le \omega \le \dfrac {3\pi}{4} \ &\dfrac {3\pi}{4} \le |\omega | \le \pi
\end{align*} \] Determine the filter coefficient h(n) by using Hamming window.
10 M
6 (b)
A one state decimator is characterised by the following decimator factor = 3 Antialising filter coefficient
h(0) = -0.06 = h(4)
h(1) = 0.30 = h(3)
h(2) = 0.62
Given the data x(n) with a successive [6, -2, -3, 8, 6, 4, -2]. Calculate and list filtered output w(n) and the output of the decimator y(n).
h(0) = -0.06 = h(4)
h(1) = 0.30 = h(3)
h(2) = 0.62
Given the data x(n) with a successive [6, -2, -3, 8, 6, 4, -2]. Calculate and list filtered output w(n) and the output of the decimator y(n).
10 M
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