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I want to see the frequency response of 1024 order bandpass filter in MATLAB.

The sampling frequency is 16kHz and the pass band frequency is [376Hz 480Hz]. I have implemented the bandpass filter using inbuilt function fir1 as b1 = fir1(1024,[376/8000 480/8000],'bandpass').
To plot the frequency response of the filter, I have used the inbuilt function freqz(b1,1,10000,16000).

My doubt is -3dB frequency obtained from the MATLAB plot should be at the pass band cut off frequency i.e at 376Hz and 480Hz right?enter image description here

Now I tried to plot the magnitude response using fdatool in MATLAB, by providing the following details: FIR equiripple filter was selected order=1024 Fs=16000 Fstop1=256 Fpass1=376 Fpass2=480 Fstop2=600 Wstop1=1 Wpass=1 Wstop2=1 and the plot obtained was as below:

enter image description here

There is difference in the frequency response

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  • $\begingroup$ You edited your question as I was answering. Originally, you were using a order N = 128 FIR filter and wondering why the cut-off was not at -6dB. Seems you've figured out you needed to increase the order to get the desired result. Hopefully my answer still explains why ;) $\endgroup$
    – Jdip
    Oct 10, 2022 at 7:00
  • $\begingroup$ Why is the frequency response obtained using Matlab fdatool showing normalized gain of 0dB at passband cut off frequencies $\endgroup$
    – Deepa
    Oct 10, 2022 at 8:55
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    $\begingroup$ You're using an equiripple design. That's a different method. Change to window method and you'll get your -6dB back if you feel like it ;) $\endgroup$
    – Jdip
    Oct 10, 2022 at 16:12

1 Answer 1

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fir1 designs FIR filters using the window method. Per the documentation:

The cutoff frequency is the frequency at which the normalized gain of the filter is –6 dB.

However, for the cut-off you specify to be at -6dB, you need to have appropriate transition bandwidth. I'm assuming you know what the window method for designing FIR filters is. If you don't, I suggest you study some examples.

Long story short, the transition bandwidth is related to the design window's main-lobe width, which is itself related to the design window's length.
For example, fir1 uses a hamming window by default, which has main lobe width of $8\pi/M$, $M$ being the length of the window.

The smaller $M$ is, the larger your transition bandwidth is.
As a matter of fact, you can estimate that the first side lobes on either part of the main lobe will have peaks at approximately $\omega_l - 1/2 \cdot8\pi/ M$ and $\omega_h + 1/2 \cdot8\pi/ M$, $\omega_l$ and $\omega_h$ being the cut-off frequencies for your band-pass. (Note: $\pi$ is the normalized nyquist frequency, so replace with $f_s/2 = 8000$ in your case)

Here are a few examples using your specs. Notice with $M$ increasing, the transition band sharpens, and you get closer to that $-6$dB at $376\, Hz$ and $480 \, Hz$ you're looking for.

enter image description here

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    $\begingroup$ @Deepa did jdip answer your question to your satisfaction? $\endgroup$ Dec 9, 2022 at 15:04
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    $\begingroup$ @DanBoschen won't notify if the user hasn't commented on the post itself $\endgroup$ Dec 10, 2022 at 12:04

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