3.2.1. Fixed-Point Variable Streaming FFTs
Log2(N) stages each containing a single butterfly unit and a feedback delay unit that delays the incoming data by a specified number of cycles, halved at every stage. These delays effectively align the correct samples at the input of the butterfly unit for the butterfly calculations. Every second stage contains a modified radix-2 butterfly whereby a trivial multiplication by j is performed before the radix-2 butterfly operations.
The following scheduled operations occur in the pipeline for an FFT of length N = 16.
- For the first 8 clock cycles, the samples are fed unmodified through the butterfly unit to the delay feedback unit.
- The next 8 clock cycles perform the butterfly calculation using the data from the delay feedback unit and the incoming data. The higher order calculations are sent through to the delay feedback unit while the lower order calculations are sent to the next stage.
- The next 8 clock cycles feed the higher order calculations stored in the delay feedback unit unmodified through the butterfly unit to the next stage.
Subsequent data stages use the same principles. However, the delays in the feedback path are adjusted accordingly.