Definitions for "Fourier Transform"
Keywords:  fft, sine, cosine, sinusoids, transform
Description and detailed explanation on Fourier Transform, some FFT, LPC etc. Runable project demonstrates DCT transform on continuous audio, show and edit audio source with different zooming and view.
A mathematical procedure that changes "time" information into "frequency" information.
The Fourier transform of an object is the transformation to the Fourier basis. If the object comprises pixels or voxels, the Fourier basis also has components. Given a dimensional object vector , the components in the Fourier basis are obtained by multiplying by the DÃ—D unitary matrix . In the simple case where all the array sizes of the object are equal to , the elements of are given by Fq r = exp( i 2Ï€ qâ‹…r / N ) / âˆšD. For general rectangular arrays, qâ‹…r / N is replaced by qx rx / Nx + qy ry / Ny + .... In keeping with standard notation, the Fourier transform of is denoted in this glossary by F(A).
a linear relationship, but this should not be confused with possible non-linearities in the system that produces f(t)