scott wrote:
>>> This isn't quite true over the reals, even assuming you're only 
>>> looking for functions with a given period.  For example the function 
>>> which is zero everywhere except being 1 at a single point will 
>>> generate the same Fourier representation as the constant zero 
>>> function since it will have the same integrals.
>>
>> O RLY?
>>
>> My DSP textbook says the Fourier transform of the delta function 
>> yields an amplitude of 1 for all frequencies. (Whereas the Fourier 
>> transform of a zero signal would be a zero signal.)
> 
> A function that is 0 everywhere except for f(0)=1 is not a delta 
> funciton. A delta function has f(0)=infinity and when integrated it 
> gives a non-zero value (ie it has area, unlike the function Kevin 
> described).

http://en.wikipedia.org/wiki/Kronecker_delta
http://en.wikipedia.org/wiki/Dirac_delta_function

So you see, we are in fact both right, for a suitable definition of 
"delta function". (I'm going by a DSP textbook.)

The Dirac delta doesn't interest me - my signals won't ever contain 
infinity.

> Have you read:
> 
> http://en.wikipedia.org/wiki/Wavelet

I have. Multiple times. I still don't understand.

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