Spectrograms FFT
FFT: Fast Fourier Transform
The FFT is a faster version of the Discrete Fourier Transform (DFT). The FFT utilizes some clever algorithms to do the same thing as the DTF, but in much less time. The DFT is extremely important in the area of frequency (spectrum) analysis because it takes a discrete signal in the time domain and transforms that signal into its discrete frequency domain representation.
Fourier Transform can depicted as follows. (In the following graph, "x1" is the input data you want to do 'fourier transform', and the series of plots on right side is the multiple cyclic data sequence with different cycles. The stem plot at the left bottom is the graph shows the forrelation coefficient of each data pair, i.e (x1, s1), (x1,s2), (x1, s3) and so forth. This corresponds to the harmonic series. Below is an illustration of the harmonic series in musical notation.
The numbers above the harmonic indicate the number of cents' difference from equal temperament (rounded to the nearest cent). Blue notes are flat and red notes are sharp.