Design a 3rd-order highpass Butterworth filter having a normalized 3-dB frequency of $$0.5\pi$$ rad/sample. Compute its frequency response. Express the magnitude response in decibels and plot it.

[b,a] = butter(3,0.5,'high');
[h,w] = freqz(b,a);

dB = mag2db(abs(h));

plot(w/pi,dB)
xlabel('\omega / \pi')
ylabel('Magnitude (dB)')
ylim([-82 5])

Repeat the computation using fvtool.

fvtool(b,a)