jimmyjazz wrote on Wed, 01 February 2006 18:06 |
Curiousity killed the cat . . . can any of you tell me what happens to the amplitude and phase response of a finite signal when you reverse it in time?
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The FFT is a filter. It does "averaging". So does the ear behave like an FFT?
Generally the ear does not behave like an FFT. Say we take a 1 second long FFT, for 2 cases:
Case 1: A 1KHz tone that grows from 0V to 1V linearly in 1 second.
Case 2: A 1KHz tone that starts at 1V and linearly decreases to 0 in 1 second.
The 2 cases will yield the same plot - the energy content of the signal over the FFT duration. Of course we expect to see energy at 1KHz, but we will also see some energy due to the modulation (the increase or decrease of amplitude).
Note: In practice, we will likely window the FFT to help deal with sudden start and stop conditions of such signal which requires infinite bandwidth.
The point is: Running a signal backwards is not a practical issue, but will yield the same amplitude vs frequency plot.
Running the "amplitude envelope" backwards is practical and will also yield the same FFT plot.
Another case: Say you take a 10 second FFT (very long), in which the signal is all very quite (9 seconds of no signal) but there is a very loud 1 second gun shot say at the "middle of the signal". The FFT will not show that the energy was concentrated over a short time (1 second). It will seem as if the gunshot sound was 10 second long at 1/10 the amplitude...
So when does the ear behave "sort of like an FFT"? That is a psychoacoustic question. The ear has it's own time window (frequency bandwidth) of response. The ear "knows" that a 1 second gun shot is not "smeared" over 10 seconds, but the ear does some averaging over short time periods (in the milliseconds or more).
But that is not my area of expertize. People that deal with audio data compression know a lot more about it...
Regards
Dan Lavry
www.lavryengineering.com