So far you've seen the FFT implemented by decimating the signal in the time domain. It is also possible to implement the FFT by decimating the signal in the frequency domain.
With this method you start decimating the signal in the frequency domain and recombine the signal in the time domain. Apart from that difference it follows the same pattern as the decimation in time method.
The first stage is breaking the N point signal down into two N/2 point DFTs.
Compare this to the DFT diagram to see how the breakdown & recombination
has been reversed. Just the same as the Decimation in Time method, the
breakdown is continued until it reaches a series of two point DFTs such
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