what do you get in you add an infinite number of sine waves, each with a unique frequency, and all of the same amplitude? not sure if pic is related.
like, if you combine all colors of light the result would be white light. but what does the waveform look like?
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sorry, typo
> what do you get in you add ...
> what do you get when you add ...
a delta function... i.e. a spike
the "waveform of white light" has nothing to do with the actual light waves involved and everything to do with your perception of them. White is three separate wavelengths that when interpreted simultaneously appear to be white.
but if those three waves (lets say red, green, and blue) combine to produce a fourth wave, wouldn't that fourth wave be "white"? if not white, what would it be?
thanks! is there some theorem or proof that shows this? is this just math 101 or signal processing? where can i read about this specific phenomenon?
Are you looking for a countable or uncountable number of frequencies? The answer is slightly different in either case.
This is true if you integrate over all frequencies, OP asked a slightly different question
white light is defined as a a collection of frequencies such that their fourier transform represents a white noise statistical distribution. the only involvement of 3 colors is due to the fact that our eyes can only probe 3 of the endless number of EM frequencies. there is nothing physically fundamental about red, green, and blue.
> ...countable or uncountable number of frequencies?
don't know. would like to hear both explanations.
>countable or uncountable number of frequencies
This occurred to me, as well. Fourier series is
countable multiples of the base frequency,
whereas white light is a continuum of
frequencies (we suppose, but maybe not?)
so perhaps we should expect a difference
between the two approaches.
The fourier transform is the uncountable analog of the countable fourier series. If you are interested in engineering, you can stop with the fourier series. The fourier integral will not be of use to you unless you a signal analysis theoretician.