Pipeline FFT architecture
A pipeline FFT is composed of five primary building blocks. The rpoint DFT or Radixr butterfly, delay units, the twiddle factor multiplier, twiddle factor ROM(s), and the commutator (switch).
Three classes of pipelines will be examined below, each is independent of the butterfly and twiddle factor ROMs. The differences between the architectures stems from the structure of the commutator and thus controls, and delay lengths.
Multipath Delay Commutator (MDC)
The most straightforward pipeline for the FFT, switches and delays multiplex and hold data in order to endure that data is ordered and arrive simultaneously as appropriate for the butterfly element. This structure results in a delay in processing equal to the time required to provide the last r sample of the RadixR butterfly for the first R samples. It provides the fastest processing speed among the pipelines discussed with a processing time Tfft of:
The tradeoff for this performance is the low utilization of processing elements, with a utilization rate of merely 1/r for each butterfly. It is also the most expensive of the architectures in terms of space.
Single path Delay Feedback Commutator (SDF)
Designed to reduce the number of delay elements required the SDF takes one half of the butterfly outputs and feeds them back into the input providing each butterfly with a feedback. Its utilization is the same as the MDC, but because it operates as a single path pipeline the processing speed time Tfft rises by a factor of r.
Single path Delay Commutator (SDC) Only applicable to Radix4, the SDC is a simplified Radix4 pipeline that produces a higher utilization of elements. Instead of a parallel processing of outputs at each butterfly it operates as a single output requiring processing of data four times as frequently as the MDC and thus achieving a 4*(1/4)=100% utilization for the butterflies. However this significant improvement in utilization requires more delay elements than in the MDC pipeline. Due to the single output nature the processing time is the same as that for a SDF.

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