Altera FFT MegaCore Function - Manual (Page 25)

Fixed-Point Variable Streaming FFTs
Fixed point variable streaming FFTs implements a radix-2 2 single delay feedback. It is similar to radix-2
single delay feedback. However, the twiddle factors are rearranged such that the multiplicative complexity
is equivalent to a radix-4 single delay feedback.
Log
2
(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 output of the pipeline is in bit-reversed order.
The following scheduled operations occur in the pipeline for an FFT of length N = 16.
1. For the first 8 clock cycles, the samples are fed unmodified through the butterfly unit to the delay
feedback unit.
2. 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.
3. 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.
Floating-Point Variable Streaming FFTs
floatin-point variable streaming FFTs implments a mixed radix-4/2, which combines the advantages of
using radix-2 and radix-4 butterflies.
The FFT has
ceiling(log 4 (N))
stages. If transform length is an integral power of four, a radix-4 FFT
implements all of the
log 4 (N)
stages. If transform length is not an integral power of four, the FFT
implements
ceiling(log 4 (N)) 1
of the stages in a radix-4, and implements the remaining stage using a
radix-2.
Each stage contains a single butterfly unit and a feedback delay unit. The feedback delay unit delays the
incoming data by a specified number of cycles; in each stage the number of cycles of delay is one quarter
of the number of cycles of delay in the previous stage. The delays align the butterfly input samples
correctly for the butterfly calculations. The output of the pipeline is in index-reversed order.
Input and Output Orders
You can select input and output orders generated by the FFT.
3-2 Fixed-Point Variable Streaming FFTs
UG-FFT
2014.12.15
Altera Corporation FFT IP Core Functional Description
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