ELE541 Old Exam Problem Discrete Filters

Given the continuous signal filter,

and

1. The equivalent discrete filter H(z), with poles and zeros at the same frequencies and the same low frequency gain. The sampling frequency is 100 KHz.

2. Find the difference equation describing the filter.

H(z) = A(z-a)/[(z-1)(z-b)]

Where a = exp(-wzT)
and
b= exp(-wpT)

wp = 1e3   wp=1e5

A = 100T(1-b)/(1-a)

H(z) = Y(z)/X(z) = Az^-1(1-az^-1)/(1-z^-1)(1-bz^-1) = (aZ^-1-aAz^-2)/(1-(1+b)z^-1+bz^-2)

y(n) = (1+b)y(n-1)-by(n-2)+Ax(n-1)-aAx(n-2)

There is more information on the MATLAB simulation file for these functions.