Light and color are physical phenomena consisting of electromagnetic waves characterized by a range of frequencies (the spectrum; see the article
"Different color systems"). Our screens, meanwhile, consist of an array of luminous points (pixels) and receive information in the form of sequences of numbers (see the article "The components of our images: luminance and chrominance").
To "compact" this information efficiently, we need to establish a link between sequences of numbers and their spectral representation. Our eyes do not treat all light waves alike: some are perceived more precisely than others. Consequently, our visual system does not notice "small" discrepancies (or errors) in the high-frequency spectrum. This property is used to compress image files (see the article "The JPEG format").
Frequencies and functions
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One particular area of mathematical analysis deals with periodic functions. A real-valued function f is periodic if there exists a real number T > 0 such that, for every real number x, f (x + T) = f (x). If it exists, the smallest value T > 0 satisfying this property is called the function's period. The sine and cosine functions are elementary examples of periodic functions.
For example, let f (x) = A sin(ωx). Its period T is 2π / ω, and its frequency F is the reciprocal of this, namely F = ω / (2π). We owe to the mathematician Jean Baptiste Joseph Fourier (1768–1830) the idea of expressing any function of period T as a sum of sinusoidal functions: a Fourier series.
