Re: Fourier Transform unique?

Fred Marshall wrote:
westocl wrote:
are these signals anomalous? I may have sampled them wrong. but they
seem to have a strong sinusoidal group delay and the same FFT.

By my calculations, they don't have FFTs that look even slightly
similar.....
Now, had you asked about their *magnitudes* then that's a different
matter but not what we were talking about. They aren't equal but are
much closer.... but "close" isn't what we were talking about either.

You may have sampled *something* wrong but these sequences are what
they are. So *they* aren't "wrong" they just "are".

Fred

Oh... you did ask about magnitude AND phase... which I interpreted to
mean
Real part and Imaginary part as they should map 1:1. But, phase doesn't
map
1:1 but many:1 so we talk about "unwrapping" phase. Yet, I believe
sequences must map 1:1. Somebody more inclined that I might help out
here....

Fred



Hi Fred,
The "many:1" property of the phase doesn't stop the Fourier Transform from
being a 1:1 mapping. Say you have a point in the frequency domain with a
phase of P. This is ambiguous with a phase of P + 2 pi, P + 4 pi, and so
on. However, in the time domain this corresponds to shifting a cosine wave
by 2 pi, 4 pi, etc., which leave it unchanged. So P in the frequency
domain (with its 2 pi ambiguity) is a 1:1 match with a single waveform in
the time domain (with its 2 pi ambiguity).
Regards,
Steve
.

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