BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANIMS(Micro
Electronics)Digital Signal Processing
Assignment 2
1. Use bilinear transformation to convert the analog filter with
system function
H (s) = s+0.1(s+0.1)2+9
into a digital IIR filter. Select T = 0.1 and compare the
locations of the zeros in H (z) with the locationsof the zeros
obtained by applying the impulse invariant method in the conversion
of H (s).
2. Determine the coefficients {h (n)} for a linear-phase FIR
filter of length M = 15 which has a symmetricunit sample response
and a frequency response that satisfies the condition
Hr(2pik15
)={
1 for k = 0, 1, 2, 30 for k = 4, 5, 6, 7
3. Transform a third order Butterworth low pass filter with DC
Gain of unity and cut-off frequency of 1rad/sec into discrete
domain by impulse invariant transformation using 1 sec sampling and
obtain H(z).
4. A LTI-DTS is described by the following difference
equation.y(n) 0.6y(n 1) + 0.9y(n 2) = x(n) 0.7x(n 1);n 0; initial
rest. Find the steady state outputof the system when x(n) = 0.5 Cos
0.2n ; n 0 by evaluating the z-domain transfer function of
thesystem at a suitable point in the z-plane.
5. Design a chebyshev HPF for the following specifications.
p = 3 dB at 250 rad/secs = 30 dB at 100 rad/sec
6. Design an ideal lowpass filter with a frequency response
Hd(ej
)= 1 for pi
2 pi
2= 0 for
pi
2 pi
Find the values of h[n] for N = 11 using (a) Hanning window (b)
Hamming window. Find H(z). Plotthe magnitude response.
7. Design an ideal highpass filter with a frequency response
Hd(ej
)= 1 for pi
4 || pi
= 0 for || pi4
Find the values of h[n] for N = 11 using (a) Hanning window (b)
Hamming window. Find H(z). Plotthe magnitude response.
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