基于System Verilog的8点FFT实现

我们采用system verilog实现一个8点的基于蝶形运算单元的FFT变换，如下图，是蝶形运算单元的示意图。

然后，由于FFT涉及复数运算，因此，我们编写如下复数类型以及运算符的一个包:

`timescale 1ns / 1ps
//
// Company: 
// Engineer: 
// 
// Create Date: 2021/07/22 11:57:16
// Design Name: 
// Module Name: complex_type
// Project Name: 
// Target Devices: 
// Tool Versions: 
// Description: 
// 
// Dependencies: 
// 
// Revision:
// Revision 0.01 - File Created
// Additional Comments:
// 
//
package complex_type;    
    parameter DATA_WIDTH = 32;
    //复数结构体类型
    typedef struct {
    logic signed [DATA_WIDTH-1:0]  r;
    logic signed [DATA_WIDTH-1:0]  i;
    } Complex;
    //复数运算函数
    //定义复数乘法
    function Complex complex_mul(Complex a,Complex b);             //(a.r+i*a.i)x(b.r+i*b.i)
        Complex res;
        //为防止溢出，扩展到64位再进行乘法
        logic [2*DATA_WIDTH-1:0] expand_a_r;
        logic [2*DATA_WIDTH-1:0] expand_a_i;
        logic [2*DATA_WIDTH-1:0] expand_b_r;
        logic [2*DATA_WIDTH-1:0] expand_b_i;
        // $display("a=(%d,%d),b=(%d,%d)",a.r,a.i,b.r,b.i);
        expand_a_r={{32{a.r[31]}},a.r};
        expand_a_i={{32{a.i[31]}},a.i};
        expand_b_r={{32{b.r[31]}},b.r};
        expand_b_i={{32{b.i[31]}},b.i};
        res.r=(expand_a_r*expand_b_r-expand_a_i*expand_b_i)>>>16;
        res.i=(expand_a_r*expand_b_i+expand_a_i*expand_b_r)>>>16;
        // $display("res=(%d,%d)",res.r,res.i);
        return res;
    endfunction
    //定义复数加法
    function Complex complex_add(Complex a,Complex b);
        Complex res;
        res.r=a.r+b.r;
        res.i=a.i+b.i;
        return res;
    endfunction
    //定义复数减法
    function Complex complex_sub(Complex a,Complex b);
        Complex res;
        res.r=a.r-b.r;
        res.i=a.i-b.i;
        return res;
    endfunction
endpackage

 然后是我们的FFT模块:

`timescale 1ns / 1ps
//
// Company: 
// Engineer: 
// 
// Create Date: 2021/07/22 09:50:53
// Design Name: 
// Module Name: FFT
// Project Name: 
// Target Devices: 
// Tool Versions: 
// Description: 
// 
// Dependencies: 
// 
// Revision:
// Revision 0.01 - File Created
// Additional Comments:
// 
//

import complex_type::* ;

module FFT
#(parameter DATA_WIDTH = 32,
  parameter N = 8,
  parameter STAGE = 3)
(
input logic clk,
input logic rst,
input logic valid,
input Complex data_in [0:N-1],
output Complex data_out [0:N-1],
output logic ready
    );
logic valid_ff1;
logic valid_ff2;
logic valid_ff3;
//定义旋转因子常量
Complex WN0 = '{65536,0};           
Complex WN1 = '{46340,-46340};
Complex WN2 = '{0,-65535};
Complex WN3 = '{-46340,-46341};
//中间结果
Complex tmp [0:STAGE][0:N-1];                                          //STAGE=log2(N),为蝶形运算单元的级数
//蝶形运算
//第1级 tmp[0]-->tmp[1]
always_ff@(posedge clk)                 //第一级,蝶形单元跨度为1=2^0
for(int i=0;i>>16);
end
//第2级 tmp[1]-->tmp[2]                 
always_ff@(posedge clk)
for(int i=0;i