Decimation in Time

The DFT is defined by

where is the input signal amplitude at time , and

Note that .

When
is even, the DFT summation can be split into sums over the
odd and even indexes of the input signal:

where and denote the even- and odd-indexed samples from . Thus, the length DFT is computable using two length DFTs. The complex factors are called

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University