11.2: Various Approaches to Developing Special Methods
- Page ID
- 2029
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There are two methods which use a complex FFT in a special way to increase efficiency. The first method uses a length-N complex FFT to compute two length-N real FFTs by putting the two real data sequences into the real and the imaginary parts of the input to a complex FFT. Because transforms of real data have even real parts and odd imaginary parts, it is possible to separate the transforms of the two inputs with 2N-4 extra additions. This method requires, however, that two inputs be available at the same time.
The second method uses the fact that the last stage of a decimation-in-time radix-2 FFT combines two independent transforms of length N/2 to compute a length-N transform. If the data are real, the two half length transforms are calculated by the method described above and the last stage is carried out to calculate the total length-N FFT of the real data. It should be noted that the half-length FFT does not have to be calculated by a radix-2 FFT. In fact, it should be calculated by the most efficient complex-data algorithm possible, such as the SRFFT or the PFA. The separation of the two half-length transforms and the computation of the last stage requires \(N-6\) real multiplications and