freqz() not behaving as expected?

I have noticed something abnormal about freqz() not as expected. For example, I want to plot a response of a delay z^-n, so I put in this code:

b = 1;

a = [1 0 0 0];

[h,w] = freqz(b, a, 1000);

plot(w, angle(h));

I expect to get a linear phase slope waveform of sawtooth. Instead I got a flat line at 0.

Also, I try to plot the phase response of an integrator:

b = 1;

a = [1 -1];

[h,w] = freqz(b,a,1000);

plot(w, angle(h));

grid;

I expect to get a phase line sloping down starting from -pi/2 to -pi. Instead it plots a line slopping up. This is strange.

Answer 1

[Paul]

The b and a inputs to freqz are the coefficients in ascending powers of z^-1. So this case

b = 1;
a = [1 0 0 0];

really means:

H(z) = 1/(1 + 0*z^-1 + 0z^-2 + 0*z^-3) = 1,

which is exactly what freqz produces

figure
freqz(b, a, 1000);

If you want H(z) = z^-3, then we'd have

b = [0 0 0 1];
a = 1;
figure
freqz(b,a,1000)

[Xiangguang]

Thanks a lot. You saved me headache.