[music-dsp] Near-nyquist signal representation

Ulrich Grassberger grasso at telebel.de
Wed Jan 29 00:11:00 EST 2003


> But wait... the lowest term of a fourier transform is
> ALWAYS the DC component... (i.e. the amount of 0Hz)
> and so the frequencies are:
> 0Hz,1Hz,2,3,4,5,6,7Hz...
> No nyquist!!
> 
> But 0Hz is constant: It has no phase...
> If the DC offset is 5, it doesn't matter where in time
> you start sampling it.
> The phase information for DC is meaningless, but the
> amplitude is not.
> 
> This means that we have one piece of information
> spare!
> 
> And what IS this information... It's half the
> information we'd need to represent the nyquist (since
> you need amplitude AND phase)! :)
> 
> So, we can represent anything BELOW nyquist, but we
> can only HALF represent the nyquist! :)
> 

That´s why they say that f + f[Nynquist] is mirrored to f + DC 
for any f >=0.

Uli




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