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Confuction with cutoff frequency

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Juan Chehin
Juan Chehin 2021-8-5
评论： Star Strider 2021-8-6
Hello, I have this code that is from a chebyshev filter and I need to know if what is marked in red on the graph corresponds to the cutoff frequencies
Fs = 4400;
Fn = Fs/2;
n = 3; Rp = 0.5;
Wn = [250 2000]/Fn;
[b a]=cheby1(n,Rp,Wn,'bandpass')
[h,w]=freqz(b,a)
plot(w,abs(h))

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Star Strider
Star Strider 2021-8-5
The first red line (at 0.357) corresponds to the low cutoff frequency. The upper cutoff frequency should be at 2.856, so the second red line (at 2.000) does not correspond to it (or to anything else of significance).
.
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Juan Chehin
Juan Chehin 2021-8-6
编辑：Juan Chehin 2021-8-6
One last question, the red line of the cutoff frequency that you put, I see that on the y axis cuts at 0.9. Shouldn't it cut at 0.707? Where the filter gain falls. Green lines
Star Strider
Star Strider 2021-8-6
Ran in:
I had to refresh my memory with respect to Chebyshev Type 1 filters.
‘The common practice of defining the cutoff frequency at −3 dB is usually not applied to Chebyshev filters; instead the cutoff is taken as the point at which the gain falls to the value of the ripple for the final time.’
So with a passband ripple defined as 0.5 dB, the cutoff frequencies correspond to that amplitude (dotted black line).
Fs = 4400;
Fn = Fs/2;
n = 3; Rp = 0.5;
Wn = [250 2000]/Fn;
[b a]=cheby1(n,Rp,Wn,'bandpass');
[h,w]=freqz(b,a,2^16);
plot(w,mag2db(abs(h)))
hold on
plot(([1;1]*Wn*pi), ([1;1]*ylim).', '-r')
plot(xlim, -0.5*[1 1], ":k")
hold off
grid
ylim([-10, 0])
legend('Passband','Cutof Frequencies', 'Location','S')
.

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