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.
maybe another way of asking is:
if you have f(x) = sin(x)+sin(2x)+sin(3x)+sin(4x)+...+sin(Nx)
what does the waveform look like when N goes to infinity? and what if N is not an integer but a real number
That is a much simpler question than the only I was just typing up in a long winded answer.
It is a divergent series. you should see the waveform deforming with a positive and negative spike. You really need a lot of linear algebra and functional analysis to give a rigorous answer though.
the top of this pdf shows the formula for the infinite sum
math.upenn.edu
and here's the graph
wolframalpha.com
doesn't look like white light to me
en.wikipedia.org
> White light is a combination of lights of different wavelengths in the visible spectrum
is it the combination of ALL visible colors/wavelengths. if so, what does the resulting waveform look like?
in your example n is the amplitude. i'm interested in adding waves of different frequencies (the amplitude can remain the same for all waves)
This is a stupid question without any answer. You get whatever you want, or nothing.
This, the question is basically "what if I add an infinite amount of random numbers between -1 and 1?" There's no answer and saying it equals 0 is ignoring the problem.
idiots dont know anything about fourier analysis
Your cone cells do not receive a fixed frequency for stimulation, but rather a small distribution. This is what can cause colourblindness; in red-green colourblindness, you end up with two pigments that respond to roughly the same frequencies, and the result is seeing brown and blue.
White light would just need to be distributed such that the frequencies that it is composed of equally stimulate your red, green, and blue pigments, so there would be an infinite number of potential white lights that could be created.
so this means that white is not a real physical color (i.e. an electromagnetic wave of a certain frequency) but is just a perceived "illusion"?
what about this
> if waves of different frequencies are not coherent, then, when combined, they create a wave that is continuous in time (e.g. white light or white noise).
en.wikipedia.org
This is bullshit. Every undergrad MechE/EEE course includes control theory where the Fourier transform and the convolution theorem is heavily used.
Control theory is a course in the subject of signal analysis. Granted, signal analysis is broad, but the Fourier Integral is not used outside of that.
This is because the Fourier Transform can be approximated with the computation of a Fourier Series. (I literally use this in my electronics research.)
t. electrical engineering researcher
bullshit. if you add sin() waves of different frequencies, they don't approach a delta function.