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What is the FOURIER TRANSFORM?
In mathematics, a Fourier transform (FT) is a mathematical transform that decomposes space- or time-dependent functions into space- or time-frequency-dependent functions.
The term Fourier transform refers both to the representation in the frequency domain and both to the mathematical operation that associates the representation in the frequency domain with a function of space or time.
The Discrete Fourier Transform (or DFT) involves taking a series of complex inputs and converting them into sine and cosine wave sums using Euler's identity (e^ix = Cos(x) +iSin(x) ).
DFT takes groups of equidistant amplitude samples at specific times and converts them to the sum of those waves. The transformed numbers encode the frequency of the phase (the "offset" of the wave), its frequency and its amplitude.
With each additional data point, you need an additional arrow of the next frequency.
After running the DFT on the inputs (using the Y axis as the complex axis and the X as the real axis), you're left with an array of complex numbers encoding the information for each frequency (which is why it's discrete) from the wave to N.
The more widespread a frequency, the greater its amplitude.
Frequency spectrum
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