Johnny B wrote on Sat, 21 May 2005 17:52 |
No one wants to do any math homework and check the stated results?
It must be almost time for the summer break, but school is not out yet, is it?
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Johnny,
I did not "check the math" and it is available at a lot of books. It is the math for Fourier SERIES, which is an analysis method suitable for STEADY STATE SIGNALS - that is a signal that is made of never ending repetition of IDENTICAL CYCLES.
Fourier series math is correct, and it was not intended for audio only. It is a very useful tool for many applications.
But the Fourier SERIES is only STEP 1. There is also the Fourier integral, a much further evolved method of enjoying ANY continues wave, over a given time period. The Fourier integral is not restricted to a "forever repetitive" wave, thus it is much better for analysing audio signals.
The math for Fourier integral is more demanding, but the flexibility in terms of ability to deal with all sorts of signals is so much greater.
The Fourier integral (which does not require steady state) is a very powerful math and engineering method to analyse almost any realistic signal, that can be expressed mathematically (be it a sine wave, a step, an FM radio signal, an impulse...
As I already answered you in another thread, the FFT is a computational analysis tool (based on collecting a "chunk of signal data), and FFT (Fast Fourier Transform) is a "subset" of Fourier analysis. It is useful when you are measuring a signal that you do not know (thus can not express mathematically).
I am repeating what I already said in this forum...
Fourier analysis is one of many tools that can be used for designing or understanding audio. I would only consider looking at audio through the eyes of the very limited Fourier series, when music becomes an infinite repetitive identical cycles....
Regards
Dan Lavry