Graphical evaluation using MATLAB `freqz' and `plot'

freqz calculates the complex response of a digital filter from the a and b coefficients of the DE . We must think of H(z) in the form :

Here eg is the greatest (negative) power of z in X(z). b(1) is the first element of a MATLAB row vector b (it is what we would normally write in these lectures).
So in our above example :

MATLAB instructions to use freqz :

b=[1,0,-1]
a=[1,0,0,0,0.25]
[H,w]=freqz(b,a,512) % do 512 frequencies in the range 0 to pi
M=abs(H)
P=angle(H)
plot(w,M,'o')        % plot amplitude response
plot(w,P,'o')        % plot phase response

Logarithmic (Bode) plots
Bode plots plot :

1. Digital frequency on a logarithmic scale
2. Amplitude on a logarithmic scale
3. Phase shift P on a linear scale

Note the application of MATLAB semilogx for such plots.