verilog 实现2阶巴特沃斯滤波器

以下是一个简单的2阶巴特沃斯滤波器的Verilog实现。其中，模块Biquad是一个二阶滤波器，模块Butterworth是一个具有多个Biquad模块的巴特沃斯滤波器。

module Biquad(
    input clk,
    input rst_n,
    input signed [15:0] x,
    output signed [15:0] y
);

parameter B0 = 1;
parameter B1 = -1.9988914;
parameter B2 = 1;
parameter A1 = 1.9988914;
parameter A2 = -0.99999999;

reg signed [15:0] w0;
reg signed [15:0] w1;
reg signed [15:0] w2;

always @(posedge clk or negedge rst_n) begin
    if (~rst_n) begin
        w0 <= 0;
        w1 <= 0;
        w2 <= 0;
    end else begin
        w0 <= x;
        w2 <= w1;
        w1 <= w0;
        y <= (B0*w0 + B1*w1 + B2*w2 - A1*y - A2*y) >> 16;
    end
end

endmodule

module Butterworth(
    input clk,
    input rst_n,
    input signed [15:0] x,
    output signed [15:0] y
);

parameter N = 2;

reg signed [15:0] w0;
reg signed [15:0] w1;
reg signed [15:0] w2;

Biquad b[N:0] (
    .clk(clk),
    .rst_n(rst_n),
    .x(x),
    .y(w0)
);

integer i;
initial begin
    w0 <= 0;
    w1 <= 0;
    w2 <= 0;
end

always @(posedge clk or negedge rst_n) begin
    if (~rst_n) begin
        w0 <= 0;
        w1 <= 0;
        w2 <= 0;
    end else begin
        for (i = 0; i < N; i = i+1) begin
            b[i].w0 <= w0;
            b[i].w1 <= w1;
            b[i].w2 <= w2;
            b[i].y <= w0;
            w0 <= b[i].y;
            w1 <= b[i].w0;
            w2 <= b[i].w1;
        end
        y <= w0;
    end
end

endmodule

这里的Biquad模块实现了一个二阶滤波器，其中B0、B1、B2、A1和A2是巴特沃斯滤波器的系数，可以根据所需的截止频率和通带/阻带响应进行计算。Butterworth模块通过将多个Biquad模块串联在一起来实现巴特沃斯滤波器。在此实现中，N参数表示滤波器的阶数。