2020-11-08_xm_real[ m ] [k[m:0] < (1<

FFT 设计

设计说明

为了利用仿真简单的说明 FFT 的变换过程，数据点数取较小的值 8。

如果数据是串行输入，需要先进行缓存，所以设计时数据输入方式为并行。

数据输入分为实部和虚部共 2 部分，所以计算结果也分为实部和虚部。

设计采用流水结构，暂不考虑资源消耗的问题。

为了使设计结构更加简单，这里做一步妥协，乘法计算直接使用乘号。如果 FFT 设计应用于实际，一定要将乘法结构换成可以流水的乘法器，或使用官方提供的效率较高的乘法器 IP。

蝶形单元设计

蝶形单元为定点运算，需要对旋转因子进行定点量化。

借助 matlab 将旋转因子扩大 8192 倍（左移 13 位），可参考附录。

为了防止蝶形运算中的乘法和加法导致位宽逐级增大，每一级运算完成后，要对输出数据进行固定位宽的截位，也可去掉旋转因子倍数增大而带来的影响。 代码如下：

`timescale 1ns/100ps
/**************** butter unit *************************
Xm(p) ------------------------> Xm+1(p)
           -        ->
             -    -
                -
              -   -
            -        ->
Xm(q) ------------------------> Xm+1(q)
      Wn          -1
*//
module butterfly
    (
     input                       clk,
     input                       rstn,
     input                       en,
     input signed [23:0]         xp_real, // Xm(p)
     input signed [23:0]         xp_imag,
     input signed [23:0]         xq_real, // Xm(q)
     input signed [23:0]         xq_imag,
     input signed [15:0]         factor_real, // Wnr
     input signed [15:0]         factor_imag,
 
     output                      valid,
     output signed [23:0]        yp_real, //Xm+1(p)
     output signed [23:0]        yp_imag,
     output signed [23:0]        yq_real, //Xm+1(q)
     output signed [23:0]        yq_imag);
 
    reg [4:0]                    en_r ;
    always @(posedge clk or negedge rstn) begin
        if (!rstn) begin
            en_r   <= 'b0 ;
        end
        else begin
            en_r   <= {en_r[3:0], en} ;
        end
    end
    //=====================================================//
    //(1.0) Xm(q) mutiply and Xm(p) delay
    reg signed [39:0] xq_wnr_real0;
    reg signed [39:0] xq_wnr_real1;
    reg signed [39:0] xq_wnr_imag0;
    reg signed [39:0] xq_wnr_imag1;
    reg signed [39:0] xp_real_d;
    reg signed [39:0] xp_imag_d;
    always @(posedge clk or negedge rstn) begin
        if (!rstn) begin
            xp_real_d    <= 'b0;
            xp_imag_d    <= 'b0;
            xq_wnr_real0 <= 'b0;
            xq_wnr_real1 <= 'b0;
            xq_wnr_imag0 <= 'b0;
            xq_wnr_imag1 <= 'b0;
        end
        else if (en) begin
            xq_wnr_real0 <= xq_real * factor_real;
            xq_wnr_real1 <= xq_imag * factor_imag;
            xq_wnr_imag0 <= xq_real * factor_imag;
            xq_wnr_imag1 <= xq_imag * factor_real;
            //expanding 8192 times as Wnr
            xp_real_d    <= {
  {4{xp_real[23]}}, xp_real[22:0], 13'b0}; 
            xp_imag_d    <= {
  {4{xp_imag[23]}}, xp_imag[22:0], 13'b0};
        end
    end
    //(1.1) get Xm(q) mutiplied-results and Xm(p) delay again
    reg signed [39:0] xp_real_d1;
    reg signed [39:0] xp_imag_d1;
    reg signed [39:0] xq_wnr_real;
    reg signed [39:0] xq_wnr_imag;
    always @(posedge clk or negedge rstn) begin
        if (!rstn) begin
            xp_real_d1     <= 'b0;
            xp_imag_d1     <= 'b0;
            xq_wnr_real    <= 'b0 ;
            xq_wnr_imag    <= 'b0 ;
        end
        else if (en_r[0]) begin
            xp_real_d1     <= xp_real_d;