🚀 go-pugleaf

David Page wrote:
> 
> I am a novice in Matlab. Please excuse if this question sounds silly.
> 
> I am experimenting with fft and ifft function of Matlab. When I take a
> fourier transform of a function, it fives me the frequency and its amplitude
> (weight of the frequency) and does not contain any information about the
> location of these frequencies.
> 
> If the above is true, how can it reconstruct the whole signal again when
> ifft is applied ? How does it remember the locations of the frequencies ?

The DFT/FFT does no time localization.  It presumes the signal is
periodic in the length of the transform and thus that all the
frequencies are infinite in temporal extent.  All that can be said about
the time of a frequency given that it is infinite in both directions is
its phase which is periodic in 2*pi.  There are other orthogonal bases
for signal decomposition than the trigonometric one Fourier found which
do not presume signal periodicity and give frequency related time
localization.  Look at wavelet theory.


Bob
-- 

"Things should be described as simply as possible, but no simpler."

                                             A. Einstein


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