At 03:43 PM 9/18/99 -0300, you wrote:
>I'm looking for a simple FFT routine for audio analisis (spectrum) that
>runs on
>low end PICs like the 16x84.
>The device have an ADC, and I need to separate the audio in 10, 7 or
>even 5 bands,
>to display it on a LCD screen or fluorescent tube, along with the signal
>intensity.
>I've seen a program that do 128 bands, and generates video, but it's too
>much for me...
>My application doesn't need to be very accurate, so any simple approach
>would work.

If you only need a feed points in the spectrum (< 10), you can get by with
a direct DFT without the fancy FFT logic.

You will need:

1. Table of 8-bit sines and cosines incremental frequencies (can store in
EEROM).
2. 8 x 8 multiply routine (available from MicroChip app note).
3. A 16-bit add routine (ditto).
4. Directly compute the coefficients via

        a(k) = sum(0,n-1) {x(k) * sin(2 pi k/n) }
        b(k) = sum(0,n-1) {x(k) * cos(2 pi k/n) }

5. You compute the power at each frequency by

        p(k) = a(k)*a(k) + b(k)*b(k)

6. If you want the rms power, you'll also need a sqrt routine. The simplest
method (albeit a slow one) is the Newton method

        s(i+1;k) = { s(i;k)*s(i;k) + p(k) }/{ 2*s(i;k) }

Note that this also requires a 8-bit into 16-bit division algorithm.

This is an interesting little problem that keeps coming up in
microprocessor applications. Perhaps the low accuracy and reliance on a
arithmetic library explains why such a routine is not commonly available.

Another approach would be to switch a more microprocessor friendly
analysis, such as use of z-transforms instead of Fourier transforms.

PS. I'm writing the above from memory, so that might be a couple of details
in error. Also, I haven't worried about scaling, since I assume this is
unimportant in the application.

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Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral@lcfltd.com
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