Verilog 实现 128 位 FFT 变换：代码示例与解释

下面是一个用 Verilog 语言编写的 128 位 FFT 变换的示例代码：\n\nverilog\nmodule fft_128bit (\n input wire clk,\n input wire reset,\n input wire [127:0] x_in,\n output wire [127:0] x_out\n);\n\nparameter N = 128;\nparameter LOG2N = 7;\n\nreg [15:0] twiddle_real [0:N/2-1];\nreg [15:0] twiddle_imag [0:N/2-1];\n\nwire [15:0] x_real [0:N-1];\nwire [15:0] x_imag [0:N-1];\n\nwire [15:0] y_real [0:N-1];\nwire [15:0] y_imag [0:N-1];\n\nwire [15:0] w_real;\nwire [15:0] w_imag;\nwire [15:0] w_imag_neg;\n\nreg [LOG2N-1:0] stage;\nreg [LOG2N-1:0] stage_count;\n\nreg [15:0] temp_real;\nreg [15:0] temp_imag;\nreg [15:0] temp_real_neg;\nreg [15:0] temp_imag_neg;\nreg [15:0] temp_real_mult;\nreg [15:0] temp_imag_mult;\n\nassign x_real[0] = x_in[15:0];\nassign x_imag[0] = x_in[31:16];\n\ngenerate\n gen_twiddle_real_imag: for (genvar i = 0; i < N/2; i = i + 1) begin\n assign twiddle_real[i] = cos(2 * $fdisplay('%f', i * 2 * pi / N));\n assign twiddle_imag[i] = -sin(2 * $fdisplay('%f', i * 2 * pi / N));\n end\nendgenerate\n\nalways @(posedge clk or posedge reset) begin\n if (reset) begin\n stage <= 0;\n stage_count <= 0;\n temp_real <= 0;\n temp_imag <= 0;\n temp_real_neg <= 0;\n temp_imag_neg <= 0;\n temp_real_mult <= 0;\n temp_imag_mult <= 0;\n end else begin\n if (stage_count == N/2) begin\n stage_count <= 0;\n stage <= stage + 1;\n end else begin\n stage_count <= stage_count + 1;\n end\n end\nend\n\nalways @(posedge clk or posedge reset) begin\n if (reset) begin\n temp_real <= 0;\n temp_imag <= 0;\n end else begin\n if (stage == 0) begin\n temp_real <= x_real[0];\n temp_imag <= x_imag[0];\n end else begin\n if (stage_count == 0) begin\n temp_real <= y_real[stage-1];\n temp_imag <= y_imag[stage-1];\n end else begin\n if (stage_count < N/2) begin\n temp_real <= y_real[(stage-1)*2+stage_count];\n temp_imag <= y_imag[(stage-1)*2+stage_count];\n end else begin\n temp_real <= y_real[(stage-1)*2+stage_count-N/2] + w_real;\n temp_imag <= y_imag[(stage-1)*2+stage_count-N/2] + w_imag;\n end\n end\n end\n end\nend\n\nalways @(posedge clk or posedge reset) begin\n if (reset) begin\n temp_real_neg <= 0;\n temp_imag_neg <= 0;\n end else begin\n if (stage == 0) begin\n temp_real_neg <= x_real[0];\n temp_imag_neg <= x_imag[0];\n end else begin\n if (stage_count == 0) begin\n temp_real_neg <= y_real[stage-1];\n temp_imag_neg <= y_imag[stage-1];\n end else begin\n if (stage_count < N/2) begin\n temp_real_neg <= y_real[(stage-1)*2+stage_count];\n temp_imag_neg <= y_imag[(stage-1)*2+stage_count];\n end else begin\n temp_real_neg <= y_real[(stage-1)*2+stage_count-N/2] - w_real;\n temp_imag_neg <= y_imag[(stage-1)*2+stage_count-N/2] - w_imag;\n end\n end\n end\n end\nend\n\nalways @(posedge clk or posedge reset) begin\n if (reset) begin\n temp_real_mult <= 0;\n temp_imag_mult <= 0;\n end else begin\n if (stage == 0) begin\n temp_real_mult <= x_real[0];\n temp_imag_mult <= x_imag[0];\n end else begin\n if (stage_count == 0) begin\n temp_real_mult <= y_real[stage-1];\n temp_imag_mult <= y_imag[stage-1];\n end else begin\n if (stage_count < N/2) begin\n temp_real_mult <= y_real[(stage-1)*2+stage_count];\n temp_imag_mult <= y_imag[(stage-1)*2+stage_count];\n end else begin\n temp_real_mult <= y_real[(stage-1)*2+stage_count-N/2] * twiddle_real[stage_count];\n temp_imag_mult <= y_imag[(stage-1)*2+stage_count-N/2] * twiddle_imag[stage_count];\n end\n end\n end\n end\nend\n\nalways @(posedge clk or posedge reset) begin\n if (reset) begin\n w_real <= 0;\n w_imag <= 0;\n end else begin\n w_real <= temp_real_mult;\n w_imag <= temp_imag_mult;\n end\nend\n\nalways @(posedge clk or posedge reset) begin\n if (reset) begin\n x_out <= 0;\n end else begin\n if (stage_count < N/2) begin\n x_out[stage*16-1:stage*16-16] <= temp_real;\n x_out[stage*16+15:stage*16] <= temp_imag;\n else begin\n x_out[stage*16-1:stage*16-16] <= temp_real_neg;\n x_out[stage*16+15:stage*16] <= temp_imag_neg;\n end\n end\nend\n\nendmodule\n\n\n这个代码实现了一个带有时钟和复位输入的 FFT 变换模块。输入信号 x_in 是一个 128 位的复数，实部和虚部各占 16 位。输出信号 x_out 也是一个 128 位的复数，实部和虚部各占 16 位。\n\n该 FFT 变换模块使用蝶形运算算法来计算 FFT 变换。在每个时钟周期中，根据当前的阶段和阶段计数，选择合适的输入数据和旋转因子进行计算。计算结果存储在临时变量中，并在下一个时钟周期中更新到输出信号 x_out 中。\n\n该代码中使用了一个参数化的 N 变量来指定 FFT 变换的大小，这里设置为 128。参数 LOG2N 是 N 的以 2 为底的对数。\n\n在 generate 块中，使用循环生成了 twiddle_real 和 twiddle_imag 数组，用于存储旋转因子的实部和虚部。\n\n这个代码只是一个示例，可能需要根据具体的需求进行修改和优化。