[sdiy] Fourier Analysis Question

[ASSI]

On Friday 17 December 2010, Tom Wiltshire wrote:
> Can you break one long fourier analysis result into an approximate copy
> based on a series of lower resolution fourier analyses without going
> back to the time domain?

Short answer: yes, but it may not be what you want to do.

Slightly longer answer: the "series of lower resolution fourier analysis" 
would be a windowed short-time FT.  That is a multiplication of the time 
domain waveform with a suitable window function, which in the frequency 
domain translates into folding the FT of the window function with the FT of 
the waveform (which you already have).  For long enough window functions and 
signals it is actually more efficient to implement the folding operation 
with (wait for it) an FFT, that is in (a possibly scaled version of) the 
time domain.

Browse around Stephan M. Bernsee's (formerly known as Stephan Sprenger) site 
http://www.dspdimension.com/ for a lot more info than I could possibly give.


Achim.
-- 
+<[Q+ Matrix-12 WAVE#46+305 Neuron microQkb Andromeda XTk Blofeld]>+

Factory and User Sound Singles for Waldorf Q+, Q and microQ:
http://Synth.Stromeko.net/Downloads.html#WaldorfSounds