### Decimation in Time

The DFT is defined by

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

*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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