Matlab: Frequency response and pole-zero plot of a 1000-Hz Butterworth lowpass filter

The following Matlab code shows the magnitude and phase response and the Z-plane of a 1000-Hz Butterworth lowpass filter.

clc;clear;close all;

Fs = 8000;  %Sampling frequency
Fco = 1000; %Cutoff frequency
order = 4;
[b, a] = butter(order, Fco/(Fs/2), 'low');

zplane(b,a);title(['LPF Fco=',num2str(Fco),'Hz, Fs=',num2str(Fs),'Hz']);

w = 0:0.01:2*pi;

H = freqz(b, a, w);

mag = abs(H);
pha = angle(H);

figure
subplot(211);
plot(w,mag);title('Magnitude');xlabel('rad/s');
subplot(212)
plot(w,pha);title('Phase');xlabel('rad/s');

figure
w_Hz = w*Fs/(2*pi); %frequency in unit of Hz.
subplot(211);
plot(w_Hz,mag);title('Magnitude');xlabel('Hz');
subplot(212)
plot(w_Hz,pha);title('Phase');xlabel('Hz');

Result:

Pole-zero plot

Magnitude and phase responses with frequency in rad/s.

Magnitude and phase responses with frequency in Hz.

References:

How to plot the magnitude and phase of a given transfer function(z-domain)?
Pole-Zero plots of various filters
draw the Pole-Zero plot of the Z-transform