The FFT core computes an
N
-point forward DFT or inverse DFT (IDFT) where
N
can be 2
m
,
m
= 3–16.
For fixed-point inputs, the input data is a vector of N complex values represented as dual b x -bit twos-complement numbers, that is, b x bits for each of the real and imaginary components of the data sample, where b x is in the range 8 to 34 bits inclusive. Similarly, the phase factors b w can be 8 to 34 bits wide.
For single-precision floating-point inputs, the input data is a vector of N complex values represented as dual 32-bit floating-point numbers with the phase factors represented as 24- or 25-bit fixed-point numbers.
All memory is on-chip using either block RAM or distributed RAM. The N element output vector is represented using b y bits for each of the real and imaginary components of the output data. Input data is presented in natural order and the output data can be in either natural or bit/digit reversed order. The complex nature of data input and output is intrinsic to the FFT algorithm, not the implementation.
Three arithmetic options are available for computing the FFT:
• Full-precision unscaled arithmetic
• Scaled fixed-point, where you provide the scaling schedule
• Block floating-point (run time adjusted scaling)
The point size N , the choice of forward or inverse transform, the scaling schedule and the cyclic prefix length are run time configurable. Transform type (forward or inverse), scaling schedule and cyclic prefix length can be changed on a frame-by-frame basis. Changing the point size resets the core.
Four architecture options are available: Pipelined Streaming I/O, Radix-4 Burst I/O, Radix-2 Burst I/O, and Radix-2 Lite Burst I/O. For detailed information about each architecture, see Architecture Options .
The FFT is a computationally efficient algorithm for computing a Discrete Fourier Transform (DFT) of sample sizes that are a positive integer power of 2. The DFT
of a sequence
is defined as
where
N
is the transform size and
. The inverse DFT (IDFT) is given by
