Some Discrete Fourier Transform Pairs
Note | ||
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Shift theorem | ||
Real DFT | ||
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from the geometric progression formula | |
from the binomial theorem | ||
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is a rectangular window function of W points centered on n=0, where W is an odd integer, and is a sinc-like function (specifically, is a Dirichlet kernel) |
Discretization and periodic summation of the scaled Gaussian functions for . Since either or is larger than one and thus warrants fast convergence of one of the two series, for large you may choose to compute the frequency spectrum and convert to the time domain using the discrete Fourier transform. |
Read more about this topic: Discrete Fourier Transform
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