IFFT with Symmetric Input in System Generator

The FFT/IFFT of real data input is symmetric: X(N-k) = X*(k). The FFT/IFFT of data with X(N-k) = X*(k) symmetry may not be real numbers unless X(0) is real and X(N/2) is real (this is implied by the symmetry equation X(N-N/2) = X*(N/2) ).

When the FFT core (view all Xilinx documents in Document Navigator) is used in SysGen to calculate the IFFT of symmetric input, there are a couple of more things to consider.

Set up FFT core for inverse FFT 

The FFT core needs to be set to IFFT mode by writing 0 to s_axis_config_tdata_fw_inv input through the AXI configuration interface PRIOR to the start of frame (see the constant blocks in the red circle below)

Starting index difference between Matlab and FFT
In Matlab, the array index starts from 1, while the index for FFT equations starts from 0. When the symmetric data input to the FFT core is created manually from a script, make sure this starting index difference is accounted for. Using an 8-point FFT as an example, the input array fft_in(1:8) should be set up like the below:

    Sample 0:   fft_in(1) = real

    Sample 1,7: fft_in(2) = conj(fft_in(8))

    Sample 2,6: fft_in(3) = conj(fft_in(7)) 

    Sample 3,5: fft_in(4) = conj(fft_in(6)) 

    Sample 4:   fft_in(5) = real

Input data range of FFT core

The FFT block in SysGen expects the input data to be in the range [-1, 1) or a N bit fixed point with N-1 fractional bits, so make sure the input samples are properly scaled to [-1,1) when they are generated in the script.

Exampe

An example with 256-point FFT block set to compute IFFT can be downloaded here. The input samples are symmetric (i.e. X(N-k) = X*(k)). Below are the magnitudes of the real and imaginary parts of the IFFT outputs, where the imaginary part is negligible (i.e. the IFFT outputs are real.).

max_abs_real_fft_sg =
    0.0078

max_abs_imag_fft_sg =
  3.5763e-007