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?

Answer

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.