### 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:

 (A.1)

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 twiddle factors. The splitting into sums over even and odd time indexes is called decimation in time. (For decimation in frequency, the inverse DFT of the spectrum is split into sums over even and odd bin numbers .)

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