STUPIDSID
1 (a)
Transfer functions of casual and stable digital filters are given below. State whether these filtes are
Minimum/ Maximum/ Mixed Phase filters
(i) H1(Z)=(1−12z)(1−14z)(z−13)(z−15)
(ii) H2(Z)=(1−12z)(z−14)(z−13)(z−15)
(iii) H3(Z)=(z−12)(z−14)(z−13)(z−15)
Minimum/ Maximum/ Mixed Phase filters
(i) H1(Z)=(1−12z)(1−14z)(z−13)(z−15)
(ii) H2(Z)=(1−12z)(z−14)(z−13)(z−15)
(iii) H3(Z)=(z−12)(z−14)(z−13)(z−15)
5 M
1 (b)
Compute DFT of the sequence X1,(n) = {1,2,4,2} using property and not otherwise compute DFT of x2(n) = {1+j, 2+2j, 4+4j, 2+2j}
5 M
1 (c)
The impulse response of a system is h(n)=anu(n), a≠0. Determine a and sketch pole zero plot for this system to act as :-
(i) Stable low pass filter. (ii) Stable High pass filter.
(i) Stable low pass filter. (ii) Stable High pass filter.
5 M
1 (d)
Draw direct form structure for a filter with transfer function, H(z) = 1+3z-1 + 2z+-3 - 4z-4
5 M
2 (a)
Consider a filter with impulse response, h(n)={0.5, 1, 0.5}. Sketch its amplitude spectrum. Find its response to the inputs
(i) x1(n)=cos(nπ2)
(ii) x2(n)=3+2δ(n)−4cos?(nπ2)
(i) x1(n)=cos(nπ2)
(ii) x2(n)=3+2δ(n)−4cos?(nπ2)
10 M
2 (b)
Determine circular convolution of x(n)= {1,2,1,4} and h(n)= {1,2,3,2} using time domain convolution and radix -2FFT. Also find circular correlation using time domain correlation.
10 M
3 (a)
Explain overlap and add method for long data filtering. Using this method find output of a system with impulse response, h(n)= {1,1,1} and input x(n)= {1,2,3,3,4,5}.
10 M
3 (b)
Compute Dft of a sequence, x(n)= {1,2,2,2,1,0,0,0} using DIF-FFT algorithm. Sketch its magnitude spectrum.
10 M
4 (a)
Draw lattice filter realization for a filter with the following transfer function.
H(Z)=11+1324z−1+58z−2+13z−3
H(Z)=11+1324z−1+58z−2+13z−3
10 M
4 (b)
Design a low pass Buttre worth filter with order 4 and passband cut off frequency of 0.4π. Sketch pole zero plot. Use Bilinear transformation. Draw direct form II structure for the designed filter.
10 M
5 (a)
Design a FIR Bandpass filter with the following specifications :-
Length : 9
stop band cut off frequency : 0.7π
Use Hanning window.
Length : 9
stop band cut off frequency : 0.7π
Use Hanning window.
10 M
5 (b)
The transfer function of a filter has two poles at z=0, two zeroes at z= -1 and a dc gain of 8. Final transfer function and impulse response.
Is this a causal or noncausal filter?
Is this a linear phase filter?
If another zero is added at z=1 find transfer function and check whether it is a linear phase filter or not.
Is this a causal or noncausal filter?
Is this a linear phase filter?
If another zero is added at z=1 find transfer function and check whether it is a linear phase filter or not.
10 M
6 (a)
Transfer function of an FIR filter is given by H(z)=1-zN. Sketch pole zero plots for N=4 and N=5 prove that it is comb filter.
10 M
6 (b)
Write about frequency sampling realization of FIR filters.
10 M
7 (a)
Explain the process of decimation for reducing sampling rate of signal.
10 M
7 (b)
Compare various windows used for designing FIR filters.
10 M
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