IIR Filter

Frequency Response of a IIR Filter

Logic:

Any IIR systems the transfer function H(z) is often expressed as a ratio of polynomials such as

H(e^jw) = [ b₀+ b₁z^-1+......+b_n z^-N / a0+a1z-1+...+amz-N ] |z=e^jwt

The above equation is same as that of the general representation of z-transform. Therefore to find frequency response of IIR system we can make use of the command "freqz"

Algorithm:

1. Input the numerator coefficients
2. Input the numerator coefficients
3. Input the sampling frequency , fs
4. Calculate the Nyquist frequency npt (npt = fs/2)
5. Find the frequency response using "freqz" command

Program

%Program to find frequency response of a given IIR response

b=input ('Enter the numerator coefficients ');

a=input (' Enter the denominator coefficients');

fs=input ('Enter the sampling frequency ');

npt=fs ./2 ; % number of frequency points

freqz(b, a, npt, fs); % find frequency response