How to design a FIR filter by the -3db bandwidth?

When I try to design a FIR low-pass filter by using -3db bandwidth as the cutoff frequency, I find that the amplitude of the cutoff frequency cannot reach -3db, and I design the filter by the FDAtool, how to solve this problem or is my design method wrong? Thanks for any help you can provide.

Answer 1

[Chunru]

Generally speaking, you don't have to worry about -3dB attenuation at the cut-off. You just specify the pass-band and stop band with certain transition band.

However, if you do want to have a deired -3dB response. One appraoch is to use generalized digital Butterworth filter (IIR not FIR) as show below. There are other approaches for FIR (such as using least square methods to fit the freq response).

num = 10; den = 2; wn = 0.2;
[b, a] = maxflat(num, den, wn);
[h, w] = freqz(b, a);

plot(w/pi, 20*log10(abs(h)));grid
ylim([-10 0])
xline(0.2); yline(-3)

[斌政 刘]

Thanks for your answer，It helped me a lot.

Can I interpret it as the -3db bandwidth is more of a measurement than a definite value?

[Chunru]

You are right. Very often, the important design parameters of a filter (such as LPF) are given in the following figture, where -3db attenuation at cut-off freq (fpass) is not specified.

[斌政 刘]

Thank you so much for your patient answer, I have learned a lot.