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# Fourier Transform Result Data

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Im trying to build a sound analyzing program, and i found the Fourier Transform algorithm, but! What is the resulting data? I know its used to build a sound spectrum, but the data is not big enough to show a spectrum per sample of the sound! Please enlighten me on this one! -Anders-Oredsson-Norway-

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After applying the Fourier Transform, you will not receive a spectrum per sample of the sound. The method instead transforms your wave data from the time domain to the frequency domain (time vs. amplitude to frequency vs. amplitude). The frequency spectrum is analogous to the dancing bars you see on many stereo players, except this is a digital method of calculating it.

The output from the algorithm you use will be (frequency, amplitude). As an example, if your input is a periodic sine wave with frequency x Hz, then your output will have a single spike at x (because an amplitude is only present in the original wave at a frequency x). If your input is a square wave, then your output will be an infinite series of spikes decreasing in amplitude spaced a bit from each other.

If you sum all of the sine waves from the outputs together (plus their phase shifts, the imaginary numbers), then you should receive a function (albeit a complicated one) that depicts the original waveform.

Danny

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is the result of an FFT at a given a given freq. linear power ? or is it logarithmic power?

since I'm on the subject- how many input points should one use for the FFT- 1024? or- I should ask, what is the comp time of the FFT versus the number of input points? I want to say N log N or something- just can't remember... =/

Edited by - Ranger_One on January 12, 2002 5:16:43 PM

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If you implement a Fourier Transform using the FFT algorithm, the number of input points must be a power of two (thus, 1024 would be acceptable). You''re right on the computational time - it is N log (N), N being the number of input points.

As for the result, It''s a linear power ... I had to multiply my x-scale (frequency) by (samples per sec/data size) (or vice versa?) to get the frequency to match correctly.

Danny

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