FFT verilog实现

FFT（快速傅里叶变换）是一种用于数字信号处理的重要算法，可以将信号从时域转换到频域。在FPGA中实现FFT可以提高信号处理的速度和效率。下面是一个用Verilog实现FFT的简单示例。

首先，需要定义FFT的输入和输出。输入是时域信号，输出是频域信号。假设输入信号的长度为2^n，输出信号的长度也为2^n。

module fft(input clk, input rst, input signed [15:0] x_i, input signed [15:0] x_q, output reg signed [15:0] y_i, output reg signed [15:0] y_q);

其中，x_i和x_q是输入信号的实部和虚部，y_i和y_q是输出信号的实部和虚部。

接下来，需要定义FFT算法中的基本运算——蝴蝶运算。蝴蝶运算是FFT算法中的基本操作，可以将输入信号分成两部分，进行复数运算，然后合并成输出信号。

module butterfly(input signed [15:0] a_i, input signed [15:0] a_q, input signed [15:0] b_i, input signed [15:0] b_q, output reg signed [15:0] c_i, output reg signed [15:0] c_q, output reg signed [15:0] d_i, output reg signed [15:0] d_q);

其中，a_i、a_q、b_i和b_q是输入信号的实部和虚部，c_i、c_q、d_i和d_q是输出信号的实部和虚部。

下面是一个简单的FFT算法的Verilog代码：

module fft(input clk, input rst, input signed [15:0] x_i, input signed [15:0] x_q, output reg signed [15:0] y_i, output reg signed [15:0] y_q);
parameter N = 8; // 输入信号长度为2^N
reg signed [15:0] x_i_r[0:N-1], x_q_r[0:N-1];
reg signed [15:0] x_i_t[0:N-1], x_q_t[0:N-1];
reg signed [15:0] y_i_r[0:N-1], y_q_r[0:N-1];
reg signed [15:0] y_i_t[0:N-1], y_q_t[0:N-1];
reg [2:0] stage = 0;
wire [2:0] addr = stage < N ? stage : stage - N;
assign x_i_t[addr] = x_i_r[addr];
assign x_q_t[addr] = x_q_r[addr];
assign y_i_t[addr] = y_i_r[addr];
assign y_q_t[addr] = y_q_r[addr];
reg [2:0] i, j, k;
reg [2:0] s, t, u, v;
always @(posedge clk) begin
if (rst) begin
x_i_r <= 0;
x_q_r <= 0;
y_i_r <= 0;
y_q_r <= 0;
stage <= 0;
end else begin
case (stage)
0: begin // 输入数据的位逆序排列
i = 0;
j = 0;
for (k = 0; k < N; k = k + 1) begin
x_i_r[k] <= x_i;
x_q_r[k] <= x_q;
y_i_r[k] <= 0;
y_q_r[k] <= 0;
end
stage <= stage + 1;
end
1: begin // 蝴蝶运算
s = 1;
for (t = 0; t < N; t = t + s) begin
for (u = t; u < t + s; u = u + 1) begin
v = u + s;
butterfly b(x_i_t[u], x_q_t[u], x_i_t[v], x_q_t[v], y_i_t[u], y_q_t[u], y_i_t[v], y_q_t[v]);
end
s = s * 2;
end
stage <= stage + 1;
end
2: begin // 输出数据的位逆序排列
i = 0;
j = 0;
for (k = 0; k < N; k = k + 1) begin
y_i <= y_i_t[k];
y_q <= y_q_t[k];
end
stage <= 0;
end
endcase
end
end
endmodule

这个FFT算法采用了蝴蝶运算实现，通过位逆序排列输入和输出数据。在实际应用中，需要根据具体的应用场景进行定制化设计和优化。