This is a pseudo-mirror of www.bores.com DSP intro at http://www.bores.com/courses/intro/filters/4_trunc.htm [sic] as per the policy of this site.
This mirror was created from the source on 03/08/2000 at 22:46 Central Time.
Commercial information, time-dependent information, and all the damn JAVA scripts have been removed.  All "htm" extensions have been changed to the proper "html" extensions.  Has also been edited for coherence, proper-linkage, and better document flow.
Copied without permission.

Introduction to DSP

Filtering

FIR filter design by the window method

FIR filter coefficients can be calculated by taking the inverse Fourier transform of the desired frequency response and throwing away the small values:

• pretend we don't mind lots of filter coefficients
• specify the desired frequency response using lots of samples
• calculate the inverse Fourier transform
• this gives us a lot of filter coefficients
• so truncate the filter coefficients to give us less
• then calculate the Fourier transform of the truncated set of coefficients to see if it still matches our requirement

BUT...

Truncating the filter coefficients means we have a truncated signal. And a truncated signal has a broad frequency spectrum:

So truncating the filter coefficients means the filter's frequency response can only be defined coarsely.

Luckily, we already know a way to sharpen up the frequency spectrum of a truncated signal, by applying a window function. So after truncation, we can apply a window function to sharpen up the filter's frequency response:

So here is an even better recipe for calculating FIR filter coefficients:

• pretend we don't mind lots of filter coefficients
• specify the desired frequency response using lots of samples
• calculate the inverse Fourier transform
• this gives us a lot of filter coefficients
• so truncate the filter coefficients to give us less
• apply a window function to sharpen up the filter's frequency response
• then calculate the Fourier transform of the truncated set of coefficients to see if it still matches our requirement

This is called the window method of FIR filter design.

BUT...

| Last updated: 10th January 2000 | http://www.bores.com/courses/intro/filters/4_trunc.htm

Telephone: 01483 740138 fax: 01483 740136 email:  Web: http://www.bores.com