用verilog写一个FFT

FFT（快速傅里叶变换）是一种常见的数字信号处理算法，可以在频域上对信号进行分析和处理。下面是一个基于Verilog的FFT实现示例，实现了8点FFT。

module fft_8 (
    input clk,
    input rst_n,
    input signed [15:0] in_real[7:0],
    input signed [15:0] in_imag[7:0],
    output signed [15:0] out_real[7:0],
    output signed [15:0] out_imag[7:0]
);

reg [15:0] twiddle_real[2:0][1:0][7:0];
reg [15:0] twiddle_imag[2:0][1:0][7:0];

reg [15:0] stage0_real[7:0], stage0_imag[7:0];
reg [15:0] stage1_real[7:0], stage1_imag[7:0];
reg [15:0] stage2_real[7:0], stage2_imag[7:0];

reg [15:0] temp_real[7:0], temp_imag[7:0];

integer i, j, k, p;

initial begin
    // 初始化旋转因子
    for (k = 0; k < 3; k = k + 1) begin
        for (p = 0; p < 2; p = p + 1) begin
            for (j = 0; j < 8; j = j + 1) begin
                twiddle_real[k][p][j] = $signed(32767 * cos((2 * $pi * p * j) / (2**k * 8)));
                twiddle_imag[k][p][j] = $signed(-32767 * sin((2 * $pi * p * j) / (2**k * 8)));
            end
        end
    end
end

// 第一级蝴蝶运算
always @(posedge clk or negedge rst_n) begin
    if (!rst_n) begin
        for (i = 0; i < 8; i = i + 1) begin
            stage0_real[i] <= 0;
            stage0_imag[i] <= 0;
        end
    end else begin
        for (i = 0; i < 8; i = i + 1) begin
            stage0_real[i] <= in_real[i];
            stage0_imag[i] <= in_imag[i];
        end
        for (i = 0; i < 8; i = i + 2) begin
            temp_real[i] = stage0_real[i] + stage0_real[i+1];
            temp_imag[i] = stage0_imag[i] + stage0_imag[i+1];
            temp_real[i+1] = stage0_real[i] - stage0_real[i+1];
            temp_imag[i+1] = stage0_imag[i] - stage0_imag[i+1];
        end
    end
end

// 第二级蝴蝶运算
always @(posedge clk or negedge rst_n) begin
    if (!rst_n) begin
        for (i = 0; i < 8; i = i + 1) begin
            stage1_real[i] <= 0;
            stage1_imag[i] <= 0;
        end
    end else begin
        for (i = 0; i < 8; i = i + 1) begin
            stage1_real[i] <= temp_real[i];
            stage1_imag[i] <= temp_imag[i];
        end
        for (i = 0; i < 8; i = i + 4) begin
            temp_real[i] = stage1_real[i] + stage1_real[i+2];
            temp_imag[i] = stage1_imag[i] + stage1_imag[i+2];
            temp_real[i+2] = stage1_real[i] - stage1_real[i+2];
            temp_imag[i+2] = stage1_imag[i] - stage1_imag[i+2];
            temp_real[i+1] = stage1_real[i+1] + stage1_real[i+3];
            temp_imag[i+1] = stage1_imag[i+1] + stage1_imag[i+3];
            temp_real[i+3] = stage1_real[i+1] - stage1_real[i+3];
            temp_imag[i+3] = stage1_imag[i+1] - stage1_imag[i+3];
        end
    end
end

// 第三级蝴蝶运算
always @(posedge clk or negedge rst_n) begin
    if (!rst_n) begin
        for (i = 0; i < 8; i = i + 1) begin
            stage2_real[i] <= 0;
            stage2_imag[i] <= 0;
        end
    end else begin
        for (i = 0; i < 8; i = i + 1) begin
            stage2_real[i] <= temp_real[i];
            stage2_imag[i] <= temp_imag[i];
        end
        for (i = 0; i < 8; i = i + 8) begin
            temp_real[i] = stage2_real[i] + stage2_real[i+4];
            temp_imag[i] = stage2_imag[i] + stage2_imag[i+4];
            temp_real[i+4] = stage2_real[i] - stage2_real[i+4];
            temp_imag[i+4] = stage2_imag[i] - stage2_imag[i+4];
            temp_real[i+1] = stage2_real[i+1] + stage2_real[i+5];
            temp_imag[i+1] = stage2_imag[i+1] + stage2_imag[i+5];
            temp_real[i+5] = stage2_real[i+1] - stage2_real[i+5];
            temp_imag[i+5] = stage2_imag[i+1] - stage2_imag[i+5];
            temp_real[i+2] = stage2_real[i+2] + stage2_real[i+6];
            temp_imag[i+2] = stage2_imag[i+2] + stage2_imag[i+6];
            temp_real[i+6] = stage2_real[i+2] - stage2_real[i+6];
            temp_imag[i+6] = stage2_imag[i+2] - stage2_imag[i+6];
            temp_real[i+3] = stage2_real[i+3] + stage2_real[i+7];
            temp_imag[i+3] = stage2_imag[i+3] + stage2_imag[i+7];
            temp_real[i+7] = stage2_real[i+3] - stage2_real[i+7];
            temp_imag[i+7] = stage2_imag[i+3] - stage2_imag[i+7];
        end
    end
end

// 输出结果
assign out_real = temp_real;
assign out_imag = temp_imag;

endmodule

这个Verilog代码实现了一个基于蝴蝶运算的FFT，其中使用了三级蝴蝶运算来实现8点FFT。输入和输出都是16位有符号整数。该实现使用了旋转因子来计算蝴蝶运算，以提高运算效率。当然，这个FFT实现只是一个简单的示例，实际应用中需要根据实际需求进行优化和修改。