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Introduction to DSP

Filtering

FIR filter design by the window method

So the filter coefficients for an FIR filter can be calculated simply by taking the inverse Fourier transform of the desired frequency response.

BUT...

• The inverse Fourier transform has to take samples of the continuous desired frequency response.
• to define a sharp filter needs closely spaced frequency samples - so a lot of them
• so the inverse Fourier transform will give us a lot of filter coefficients
• but we don't want a lot of filter coefficients

We can do a better job by noting that:

• the filter coefficients for an FIR filter are also the impulse response of the filter
• the impulse response of an FIR filter dies away to zero
• so many of the filter coefficients for an FIR filter are small
• and perhaps we can throw away these small values as being less important

Here is a better recipe for calculating FIR filter coefficients based on throwing away the small ones:

• 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...

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

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