>> 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.

Ok, well if you are dealing with discrete digital functions then the concept 
of a function having "zero area" doesn't really make any sense, so yes, any 
function can be made from a series of sine and cosines.

>> Have you read:
>>
>> http://en.wikipedia.org/wiki/Wavelet
>
> I have. Multiple times. I still don't understand.

Did you check out some of the links at the bottom?  I just read this one and 
it was ok to understand:

http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html

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