This project contains fully pipelined floating-point FFT/IFFT cores for Xilinx FPGA, Scheme: Radix-2, Decimation in frequency and decimation in time;
Integer data type and twiddles with configurable data width. Code language - VHDL, Verilog Vendor: Xilinx, 6/7-series, Ultrascale, Ultrascale+;

License: GNU GPL 3.0.

Floating point 23-bit vector (optimized for FPGAs):

• EXPONENT - 6-bits
• SIGN - 1-bit
• MANTISSA - 16+1 bits '1' means hidden bit for normalized floating-point values;

A = (-1)^sign(A) * 2^(exp(A)-31) * mant(A)

• FFTs:

  • fp23_fftNk – main core - Floating-point FFT, Radix-2, DIF, input flow - natural, output flow - bit-reversed.
  • fp23_ifftNk – main core - Floating-point FFT, Radix-2, DIT, input flow - bit-reversed, output flow - natural.

• Butterflies:

  • fp23_bfly_fwd – Floating-point butterfly Radix-2, decimation in frequency,
  • fp23_ibfly_inv – Floating-point butterfly Radix-2, decimation in time.

• Math (in fp23):

  • fp23_addsub – adder / substractor,
  • fp23_addsub_dbl – adder and substractor,
  • fp23_fix2float – int16 to fp23 converter,
  • fp23_float2fix – fp23 to int16 converter,
  • fp23_mult – multiplier,
  • fp23_cmult – complex multiplier.

• Delay line:

  • fp_delay_line – main delay line, cross-commutation data between butterflies,
  • fp23fft_align_data – data and twiddle factor alignment for butterflies in FFT core,
  • fp23ifft_align_data – data and twiddle factor alignment for butterflies in IFFT core.

• Twiddles:

  • rom_twiddle_int – 1/4-periodic signal, twiddle factor generator based on memory and sometimes uses DSP48 units for large FFTs
  • row_twiddle_tay – twiddle factor generator which used Taylor scheme for calculation twiddles.

• Buffers:

  • fp_Ndelay_in – input delay line (for simple flow with 1 data word in clock cycle),
  • fp_Ndelay_out – output delay line (for simple flow with 1 data word in clock cycle),
  • fp_bitrev_ord – converter data from bit-reverse to natural order.

• FFTs:

  • fp23_fconv_core – main core: Input buffer, Lin Fast Convolution, Output buffer, Support function,
  • fp23_linconv_dbl – Forward FFT, Inverse FFT, Complex multiplier etc,
  • fp23_fftNk2_core - Double Path Forward / Inverse Floating-point FFT, Radix-2, DIF/DIT,

• Buffers:

  • iobuf_fft_hlf2 – delay second part of data for Linear Fast Convolution,
  • iobuf_fft_int2 – delay first part of data for Linear Fast Convolution,
  • inbuf_fastconv_int2 – Input buffer for linear fast convolution and interleave-2 data,
  • int_delay_wrap - delay line for wrap-mode. You don't need collecting NFFT data words. Fully pipelined.
  • fp23_sfunc_dbl - Support function: two buffers 0/1 can store filter responce into freq domain.

• Create Vivado project example.xpr, select 7-series or Ultrascale/+ FPGA.
• Add sources from /src directory to your project.
• Set testbench file as top for simulation from /src/testbench dir directory
• Run Octave / MATLAB .m file from math/ directory. Set NFFT and other signal parameters. Change input signal or use my model. After this you will get test file test_signal.dat with complex signal.
• Run simulation into Vivado / Aldec Active-HDL / ModelSim. Set time of simulation > 100 us. For N > 32K set 500 us or more.
• Return to Octave / MATLAB and run .m script again.
• Compare Fast Convolution: an ideal result in double prec. and HDL results (fp23).

• https://habr.com/ru/post/322728/

• Kapitanov Alexander

• 2015/02/02