STUPIDSID
1 (a)
One of zeros of a causal linear phase FIR filter is at 0.5 e-ix/s. Show the locations of the zeros and hence find the transfer function and impulse response of the filter.
5 M
1 (b)
Determine Zeros of the following FIR system and indicate when the system is minimum phase maximum phase and mixed phase.
1. H(z)=6+Z-1+Z-1
2. H[z]=1-Z-1-6Z-2
1. H(z)=6+Z-1+Z-1
2. H[z]=1-Z-1-6Z-2
5 M
1 (c)
Find the number of complex multiplication and complex additions required to find DFT for 32 point sequence. Compare them with number of computation required if FFT algorithm is used.
5 M
1 (d)
What is linear phase filters. Define group delay and phase delay.
5 M
2 (a)
Derive Radix-2 Decimation in Time Fast Fourier-Transform and draw its signal flow graph.
10 M
2 (b)
X[k]={36, -4+ j 9.656, -4 + j4, -4 +j1.656, -4, -4+j1.656, -4-4j4, -4 - j9.656} Find x[n] using IFFT algorithm (use DD IFFT).
10 M
3 (a)
An 8 point sequence x[n]={1,2,3,4,5,6,7,8}
i) Find X[k] using DIF-FFT algorithm
ii) Let x1[n]={5,6,7,8,1,2,3,4} using appropriate DFT property and result of part (i) determine X1[k].
i) Find X[k] using DIF-FFT algorithm
ii) Let x1[n]={5,6,7,8,1,2,3,4} using appropriate DFT property and result of part (i) determine X1[k].
10 M
4 (a)
Design a Chetryshev I bandstop digital filter with the following specifications:
Passband range: 0 to 275 Hz and 2KHz to ?
Stopband range: 550 to 1000 Hz
Sampling frequency: 8KHz
Passband attenuation: 1dB
Stopping attenuation: 15dB Use BLT and assume T=1sec.
Passband range: 0 to 275 Hz and 2KHz to ?
Stopband range: 550 to 1000 Hz
Sampling frequency: 8KHz
Passband attenuation: 1dB
Stopping attenuation: 15dB Use BLT and assume T=1sec.
10 M
4 (b)
Design a Butterworth filter satisfying the following constraints: \[\begin {align*}
0.75 \le &|H(w)| \le 1 & for \ 0 \le w \le \pi /2 \ \ \\
& |H(w)|\le 0.2 & for \ 3 \pi /4 \le w \le \pi
\end{align*} \] Use Bilinear Transformation Method.
10 M
5 (a)
Design FIR digital highpass filter with a frequency response \[ \begin {align*}
H(w)&=1 &\pi /4 \le |w|\le \pi \\ &=0 &|w| \le \pi /4 \ \ \ \ \ \ \ \
\end{align*} \] Use Hamming window: N=7
10 M
5 (b)
With a neat diagram describe frequency sampling realization of FIR filters.
10 M
6 (a)
An FIR filter is given by the difference equation \[ y[n] = 2x[n] + \dfrac {4}{5} x [ n-1] + \dfrac {3}{2} x [ n-2] + \dfrac {2}{3} x [n-3] \] Determine the lattice form.
10 M
6 (b)
Using linear convolution find y[n] for the sequence x[n]={1,2,-1,2,3,-2,-3,-1,1,2,-1} and h[n]={1,2}. Compare the result by solving the problem using overlap save method.
10 M
Write Short Notes On:
7 (a)
Digital Resonator.
5 M
7 (b)
Parseval's Energy theorem and its significance.
5 M
7 (c)
Goertzel Algorithm.
5 M
7 (d)
Application of signal processing in RADAR
5 M
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