Colors from a computer vs. colors from visible spectrum of sunlight Observation:
So, I know that all computer screens are able to project many different colors by varying how they display the RGB (Red, Green, Blue) pixels.
Question
What's the difference between say, yellow light (575 nm) from sunlight vs. the same yellow light that's displayed on the computer screen? Aren't they different? Is our brains mixing together the RGB lights together and its being interpreted as yellow light or is yellow light the same (575 nm) light that comes from sunlight actually hits our eyes?
Relationship between Fourier Series and light?
1) So I know that in Fourier Series, you have basis functions, sines and cosines that make up any other function depending on the coefficients that are in front of the sines and cosines terms.
2) I know that RGB colors on a screen are the "basis" for all the other colors that a computer screen makes up and the intensity of each of the RGB are like the "coefficients". So, am I making the correct relationship here?
 A: If you compare at the oscillating light waveform for the yellow of the sun, and the oscillating light waveform for the similar-looking yellow of the computer screen (made of red and green pixels), the waveforms look entirely different, their Fourier transforms look entirely different, and in fact they have absolutely no mathematical relationship of any kind. The only relationship that the two waveforms have is: "both wavesforms happen to excite the three human photoreceptor cells in the same X:Y:Z ratio".
A: When you say “yellow light (575 nm) from sunlight” I assume you mean the
monochromatic light you get by sending sunlight through a narrow-band
filter centered at 575 nm. Unfiltered sunlight is not 575 nm, it's very
wide band.
The difference is then that the monitor yellow has a complex spectrum,
which is the combination of the spectra of red and green phosphors.
Visually both will look very close, although monochromatic yellow is
slightly more saturated. Its saturation can not be matched by the
monitor because, as all spectral colors, it lies outside the
monitor gamut.
Light spectra are related to the
Fourier transform
(rather than the Fourier series). The spectrum is the squared modulus of
the Fourier transform of the electromagnetic oscillation. The basis is
of infinite dimensions, because there are infinitely many possible
frequencies. Colors, on the other hand, are not really related to
Fourier transforms or series. They exist in a 3D space because our eyes
have three kinds of sensors (setting aside the rods that we use in dark
situations) called L, M and S cones (for long, medium and short
wavelengths). The only thing they can see as “color” is the combination
of how mush each of these sensors are excited. The space of colors is
much smaller than the space of spectra, therefore, most colors can be
reproduced by many different spectra.
A: the eye has 3 different photo-receptors, which are sensitive in the following spectra: 
(http://en.wikipedia.org/wiki/Color_vision)
therefore a pure frequency 575nm light triggers L highly, and M somewhat. The brain then perceives this the same as any other combination of colours which would sum to the same amount of M+L+S stimulation, eg: some light at 550nm+ lots of light at 650nm.
This question leads into a much more complex discussions about perceptual gamut and the ability to say that 2 distributions of incoming light are pecieved as "the same". (see discussion following "Mathematics of color perception" on the color vision wiki link above)
A: Yes, the mixing is happening in the eyes & brain; no, an RGB mix of yellow isn't the same as a pure yellow frequency; but our eyes will see it as the same.
The eyes have 3 (or 2, if you're colour-blind) types of colour sensors, each of which responds with a different signal profile - each peaks at a particular frequency, and trails off for frequencies that differ from that. The brain merges the signals from those 3 (or 2) different sensors, to make sense of the colour signals to create a single colour signal, and it can't tell whether that was a balanced combination of red and green, or a pure yellow frequency.
See also this answer to a previous, related question.
That explains most colours we see. Except for when we see a combination of red and blue, with no signals in between. There isn't a colour in the spectrum for that - the colours in between red and blue all feature higher signals in the middle, around green. To have signals from red and blue but not green, doesn't map to the spectrum. And our brain won't show a combination of two or more colours for a single point, it always maps a single point to a single colour.
So our brain creates a new colour, not on the spectrum, for a combination of red and blue.  Hence, purple pigments aren't real, in that sense - purple is the brain's interpolation of red + blue + no green. Purple is just a pigment of our imagination.
