# Digital LPF Using Impulse Invariance Method

See attached word file. Taken from 'Digital Signal Processing Using MatLab' by Ingle/Proakis

1. Design a digital LPF to be used in the configuration

To satisfy the following requirements:

Sampling rate = 8 kilosamples/sec

Passband edge of 1.5kHz with ripple of 3dB

Stopband edge of 2kHz with attenuation of 40dB

Equiripple Passband but monotone Stopband, and

Impulse invariance

(a) Choose T=1 in the impulse invariance method and determine the system function H(z) in parallel form. Plot the log-magnitude response in dB and the impulse response h(n).

(b) Choose T=1/8000 in the impulse invariance method and determine the system function H(z) in parallel form. Plot the log-magnitude response in dB and the impulse response h(n). Comment on the effect of T on the impulse invariance.

Please see attachment for details and question.

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#### Solution Summary

In the solution, a digital LPF is designed using matlab, given the parameters for sampling rate, passband edge, stopband edge, and type of passband. In addition, the system function is calculated with the impulse invariance method, and plots of the log-magnitude response and impulse response are given.