Number of taps vs. frequency resolution for fir filters

Dan_E10 · 19th June 2008, 01:36 PM

Apologies in advance if this has been covered before, but I couldn't find anything clearing up this question.

I'm attempting to get Ubuntu up and running with BruteFIR to do active crossovers digitally. In thinking about filter design and I'm trying to understand the number of taps required. I've seen the equation for frequency resolution: Fres = Fs/Ntaps. I'm trying to understand, does this determine the limit on the resolution of the filter frequency response that can be specified only(slope, width of peaks dips that can be equalized out, etc.)? Or does it determine some kind limit on the frequency resolution of the signal that is output from the filter? For example let's say my sample rate is 44100kHz and I use 441 taps to give a resolution of 100 Hz. If I have a signal feeding the filter that is two sine waves of frequency 325 Hz and 375 Hz, are the frequencies blurred together or distorted in some sense?
thanks,
Dan

jahonen · 19th June 2008, 03:04 PM

Dan,

more taps you'll have, sharper and steeper the frequency response can be. That formula probably derives from the Fourier transform method, where you "draw" the frequency response of the filter, and inverse Fourier transform is then performed to calculate the filter impulse response. Or, the frequency domain specification is directly used for filtering the input data using FFT.

Frequency resolution in this sense affects only frequency response, it does not distort the signal by any way. So feeding those 325 and 375 Hz signals to filter with 100 Hz frequency resolution outputs same frequencies.

Regards,
Janne

Corax · 19th June 2008, 03:40 PM

Have a look at http://www.dspguide.com/ and download chapters 14 to 21 (or even the whole book). FIR filter can be found in chapter 17.

It's a great book, written easily, with a bunch of examples. I can really recommend it for beginners, students and everybody else who's involved in this numeric audio stuff.

Dan_E10 · 20th June 2008, 08:09 PM

Thanks for the responses. That makes sense. The DSP guide looks very useful.
Dan

19th June 2008, 01:36 PM	#1
Dan_E10 diyAudio Member Join Date: May 2007	Number of taps vs. frequency resolution for fir filters Apologies in advance if this has been covered before, but I couldn't find anything clearing up this question. I'm attempting to get Ubuntu up and running with BruteFIR to do active crossovers digitally. In thinking about filter design and I'm trying to understand the number of taps required. I've seen the equation for frequency resolution: Fres = Fs/Ntaps. I'm trying to understand, does this determine the limit on the resolution of the filter frequency response that can be specified only(slope, width of peaks dips that can be equalized out, etc.)? Or does it determine some kind limit on the frequency resolution of the signal that is output from the filter? For example let's say my sample rate is 44100kHz and I use 441 taps to give a resolution of 100 Hz. If I have a signal feeding the filter that is two sine waves of frequency 325 Hz and 375 Hz, are the frequencies blurred together or distorted in some sense? thanks, Dan

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19th June 2008, 03:04 PM	#2
jahonen diyAudio Member Join Date: Jan 2002 Location: Kuopio, Finland	Dan, more taps you'll have, sharper and steeper the frequency response can be. That formula probably derives from the Fourier transform method, where you "draw" the frequency response of the filter, and inverse Fourier transform is then performed to calculate the filter impulse response. Or, the frequency domain specification is directly used for filtering the input data using FFT. Frequency resolution in this sense affects only frequency response, it does not distort the signal by any way. So feeding those 325 and 375 Hz signals to filter with 100 Hz frequency resolution outputs same frequencies. Regards, Janne

19th June 2008, 03:40 PM	#3
Corax diyAudio Member Join Date: Feb 2005 Location: south of lower saxon	Have a look at http://www.dspguide.com/ and download chapters 14 to 21 (or even the whole book). FIR filter can be found in chapter 17. It's a great book, written easily, with a bunch of examples. I can really recommend it for beginners, students and everybody else who's involved in this numeric audio stuff.

20th June 2008, 08:09 PM	#4
Dan_E10 diyAudio Member Join Date: May 2007	Thanks for the responses. That makes sense. The DSP guide looks very useful. Dan

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