r22sdf

Implementation of pipeline FFT described in Verilog HDL.

• Radix-2² single-path delay feedback (R2²SDF) architecture
• Scaled fixed-point arithmetic
• Synthesizable with FPGA implementation software

Interface

module FFT #(
    parameter   WIDTH = 16
)(
    input               clock,  //  Master Clock
    input               reset,  //  Active High Asynchronous Reset
    input               di_en,  //  Input Data Enable
    input   [WIDTH-1:0] di_re,  //  Input Data (Real)
    input   [WIDTH-1:0] di_im,  //  Input Data (Imag)
    output              do_en,  //  Output Data Enable
    output  [WIDTH-1:0] do_re,  //  Output Data (Real)
    output  [WIDTH-1:0] do_im   //  Output Data (Imag)
);

Data must be input consecutively in natural order. The result is scaled to 1/N and output in bit-reversed order. The output latency differs depending on the transform size. For 64-point FFT, it is 71 clock cycles.

64-point FFT timing diagram

Source Files

There are two kinds of configurations.

• Basic configuration for small size FFT
• Resource saving configuration for large size FFT

In my environment, when the number of FFT points is greater than or equal to 256 it is better to use the resource saving configuration.

For the basic configuration, use the following files.

FFT.v
SdfUnit.v
SdfUnit2.v
Butterfly.v
DelayBuffer.v
Multiply.v
Twiddle.v

FFT.v and Twiddle.v must be created according to the number of FFT points and the data bit length. SdfUnit2.v is required if the number of FFT points is not a power of 4. To make a resource saving configuration, replace SdfUnit.v with SdfUnit_TC.v and add TwiddleConvert4.v or TwiddleConvert8.v.

TwiddleConvert4 reduces the table size of Twiddle to 1/4. Likewise, TwiddleConvert8 reduces it to 1/8, but requires more additional logic than TwiddleConvert4. TwiddleConvert8 is used by default, but TwiddleConvert4 may be better in some cases.

Architecture

Radix-2² single-path delay feedback (R2²SDF) is known as an efficient implementation of pipeline FFT. There is radix-2 single-path delay feedback (R2SDF) in a similar architecture, but R2²SDF uses fewer multipliers.