FIR filter shortening technique

Started by MahmoodAburomoh 5 years ago6 replieslatest reply 5 years ago314 views

Hello all,

   It's my first participation here. Greetings ! 

I'm having an FIR filter with 1024 taps which represents a channel. I would like to find and equivalent 3 taps filter which gives a fair approximation for the magnitude response (I don't care much about the phase response). Does any one know a good and easy to learn technique to do so ? An accompanied matlab code will be much appreciated if available. 


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Reply by achesirJuly 11, 2019

Assuming your filter is a purely real filter (i.e. all the taps values are purely real numbers):

An N-tap FIR filter is a filter with (N-1) zeroes (the roots of the polynomial).

With 3 taps you have two choices: Either both zeroes are on the real axis, or the zeroes are complex-conjugate zeroes.

Plot the positions of the zeroes of the original 1024-tap filter in the Z-plane:

1) If the zeroes tend to cluster in a single pair of complex-conjugate locations, then in your 3-tap filter, place 1 zero in each of the two locations (once again, complex-conjugate).

2) If the zeroes tend to cluster in not more than two locations on the real axis, then in your 3-tap filter, place 1 zero in each of the two locations.

Either way, adjust the gain to a DC signal in your new filter to match the DC gain of the original 1024-tap filter.

If the zeroes of the original 1024-tap filter cluster in more than 2 locations, give up.

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Reply by JohnEhlersJuly 11, 2019

If you are only interested in an amplitude approximation, why not just use an equivalent IIR filter?

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Reply by rbjJuly 11, 2019

yeah, what John says.  because reducing 1024 degrees of freedom down to 3 degrees of freedom might not so good.  even if your FIR taps are not adjacent to each other and your delay line is longer than 3 samples.

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Reply by andrewstanfordjasonJuly 11, 2019

To be clear you want to shorten a 1024 tap FIR down to 3 taps whilst preserving the magnitude response but are willing to compromise on the phase response? 

Will you be able to cascade this 3 tap FIR filter with more 3 tap filters? Or were you thinking of just using one?

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Reply by napiermJuly 11, 2019


1024 down to 3 may be a tall order.  However, depending on your real system requirements there may be something to do.

What are the requirements?  Sample rate, min/max of the Frequency range.  If the phase response doesn't matter then is it an audio application?  That matters because of some time artifacts that the FIR is bad at.

What is the required output sample rate?  Can the signal be decimated and the filtering done at a lower rate?  What is the application?

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Reply by Rick LyonsJuly 11, 2019

Hello y MahmoodAburomoh.

You ask a strange question. Tell us, why would you want to convert a 1024-tap FIR filter to a 3-tap FIR filter?