在以往采用 FPGA 实现的 FIR 滤波功能，滤波器系数是通过 matlab 计算生成，然后作为固定参数导入到 verilog 程序中，这尽管简单，但灵活性不足。在某些需求下（例如捕获任意给定台站信号）需要随时修改滤波器的中心频率、带宽等信息，这要么通过上位机计算系数后更新到 FPGA 端（但并非所有设备都具备配套的上位机），要么直接在 FPGA 端计算并更新滤波器系数。本文对后者进行实现。
计算 FIR 滤波器系数，主要包括两个方面的计算：窗函数计算，滤波器系数计算。
窗函数生成
几种常用窗函数
首先给出几种常用的窗函数的表达式，这里不对窗函数细节进行讨论：
- 矩形窗
w ( n ) = 1.0 , n = 0 , 1 , . . . , N − 1 w(n) = 1.0,\ n=0,1,...,N-1 w(n)=1.0, n=0,1,...,N−1
- 三角窗
w ( n ) = 1 − ∣ 1 − 2 n N − 1 ∣ , n = 0 , 1 , . . . , N − 1 w(n)=1 - |1 - \frac{2n}{N - 1}|,\ n=0,1,...,N-1 w(n)=1−∣1−N−12n∣, n=0,1,...,N−1
- 图基窗 Tukey
w ( n ) = { 0.5 − 0.5 cos ( n π k + 1 ) , 0 ≤ n ≤ k 1.0 , k < n ≤ N − k − 2 0.5 − 0.5 cos ( π ( N − n − 1 ) k + 1 ) , N − k − 2 < n ≤ N − 1 , where k = N − 2 10 w(n)= \left\{ \begin{aligned} 0.5 - 0.5\cos(\frac{n\pi}{k + 1}),&\ 0\le n\le k\\ 1.0,&\ k<n\le N-k-2\\ 0.5 - 0.5\cos(\frac{\pi(N - n - 1)}{k + 1}),&\ N-k-2<n\le N-1\ \end{aligned} \right. ,\ \text{where}\ k=\frac{N-2}{10} w(n)=⎩ ⎨ ⎧0.5−0.5cos(k+1nπ),1.0,0.5−0.5cos(k+1π(N−n−1)), 0≤n≤k k<n≤N−k−2 N−k−2<n≤N−1 , where k=10N−2
- 汉宁窗 Hann
w ( n ) = 0.5 × [ 1.0 − cos ( 2 π n N − 1 ) ] , n = 0 , 1 , . . . , N − 1 w(n)=0.5 \times [1.0 - \cos(\frac{2\pi n}{N - 1})],\ n=0,1,...,N-1 w(n)=0.5×[1.0−cos(N−12πn)], n=0,1,...,N−1
- 汉明窗 Hamming
w ( n ) = 0.54 − 0.46 cos ( 2 π n N − 1 ) , n = 0 , 1 , . . . , N − 1 w(n)=0.54 - 0.46\cos(\frac{2\pi n}{N - 1}),\ n=0,1,...,N-1 w(n)=0.54−0.46cos(N−12πn), n=0,1,...,N−1
- 布莱克曼窗 Blackman
w ( n ) = 0.42 − 0.5 cos ( 2 π n N − 1 ) + 0.08 cos ( 4 π n N − 1 ) , n = 0 , 1 , . . . , N − 1 w(n)=0.42 - 0.5\cos(\frac{2\pi n}{N - 1}) + 0.08\cos(\frac{4\pi n}{N-1}),\ n=0,1,...,N-1 w(n)=0.42−0.5cos(N−12πn)+0.08cos(N−14πn), n=0,1,...,N−1
verilog 实现
可以观察到，Tukey、Hann、Hamming 和 Blackman 窗都用到了余弦函数，这可以用正余弦查找表实现，下面代码中会用到这一模块，可参考我这篇博文；窗函数生成器代码如下
/* * file : FIR_windows_generator.v* author : 今朝无言* lab : WHU-EIS-LMSWE* date : 2024-09-26* version : v1.0* description : 生成指定阶数、指定类型的窗函数*/
`default_nettype none
module FIR_windows_generator(
input wire clk,
input wire rst_n,input wire en, //上升沿触发窗口计算
input wire [3:0] win_type, //窗口类型，1:矩形窗，2:图基窗Tukey，3:三角窗，4:汉宁窗Hann，5:海明窗Hamming，6:布莱克曼窗Blackman，(7:凯塞窗kaiser, 暂未实现)
input wire [15:0] n, //窗口长度
input wire [15:0] i, //窗口索引值，0 ~ n-1
//input wire signed [15:0] beta, //kaiser窗的参数beta，win_type=7时需要这个参数，其他情况可任意给值output wire busy, //指示模块是否计算完成
output wire signed [15:0] win
);reg signed [15:0] win_buf = 16'sd256; //8-8有符号定点数
reg signed [15:0] win_buf_d0 = 16'sd256;
reg busy_buf = 1'b0;assign win = win_buf_d0;
assign busy = busy_buf;localparam S_IDLE = 4'h1;
localparam S_CAL = 4'h2;
localparam S_END = 4'h4;reg [3:0] state = S_IDLE;
reg [3:0] next_state;always @(posedge clk) beginif(~rst_n) beginstate <= S_IDLE;endelse beginstate <= next_state;end
endalways @(*) begincase(state)S_IDLE: beginif(en_pe) beginnext_state <= S_CAL;endelse beginnext_state <= S_IDLE;endendS_CAL: begincase(win_type)4'd1: begin //矩形窗next_state <= S_END;end4'd2: begin //图基窗if(cnt >= 4'd4) beginnext_state <= S_END;endelse beginnext_state <= S_CAL;endend4'd3: begin //三角窗if(cnt >= 4'd1) beginnext_state <= S_END;endelse beginnext_state <= S_CAL;endend4'd4: begin //汉宁窗if(cnt >= 4'd3) beginnext_state <= S_END;endelse beginnext_state <= S_CAL;endend4'd5: begin //海明窗if(cnt >= 4'd3) beginnext_state <= S_END;endelse beginnext_state <= S_CAL;endend4'd6: begin //布莱克曼窗if(cnt >= 4'd5) beginnext_state <= S_END;endelse beginnext_state <= S_CAL;endend// 4'd7: begin //凯塞窗 这个涉及到循环逼近bessel函数和sqrt计算，FPGA比较麻烦，就先不实现这个窗口类型了// next_state <= S_END;// enddefault: beginnext_state <= S_END;endendcaseendS_END: beginnext_state <= S_IDLE;enddefault: beginnext_state <= S_IDLE;endendcase
end//en 边沿检测
wire en_pe;
detect_sig_edge detect_sig_edge_inst(.clk (clk), //工作时钟.sig (en), //待检测信号.sig_pe (en_pe), //信号上升沿.sig_ne (), //下降沿.sig_de () //双边沿
);//cnt 控制读取cosin结果，以计算窗口值
reg [3:0] cnt = 4'd0;
always @(posedge clk) begincase(state)S_IDLE: begincnt <= 4'd0;endS_CAL: begincnt <= cnt + 1'b1;enddefault: begincnt <= 4'd0;endendcase
end//win_buf
reg signed [31:0] multi_tmp = 32'sd0;
always @(posedge clk) beginif(~rst_n) beginwin_buf <= 16'sd256; //1.0endelse case(state)S_CAL: begincase(win_type)4'd1: begin //矩形窗win_buf <= 16'sd256;end4'd2: begin //图基窗if(cnt == 4'd4) beginif(i <= k) beginwin_buf <= (16'sd256 - (cos_val_s >>> 7)) >>> 1;endelse if(i > n - k - 4'd2) beginwin_buf <= (16'sd256 - (cos_val_s >>> 7)) >>> 1;endelse beginwin_buf <= 16'sd256;endendelse beginwin_buf <= win_buf;endend4'd3: begin //三角窗if(cnt == 4'd0) beginmulti_tmp <= 16'sd512 * i / (n - 1'b1);endelse if(cnt == 4'd1) beginwin_buf <= 16'sd256 - abs(16'sd256 - multi_tmp[15:0]);endelse beginwin_buf <= win_buf;endend4'd4: begin //汉宁窗if(cnt == 4'd3) beginwin_buf <= 16'sd128 - (cos_val_s >>> 8); //0.5 * (1.0 - cos(2 * i * pi / (n - 1)));endelse beginwin_buf <= win_buf;endend4'd5: begin //海明窗if(cnt == 4'd3) beginwin_buf <= 16'sd138 - ((16'sd118 * (cos_val_s >>> 7)) >>> 8); //0.54 - 0.46 * cos(2 * i * pi / (n - 1));endelse beginwin_buf <= win_buf;endend4'd6: begin //布莱克曼窗if(cnt == 4'd3) beginwin_buf <= 16'sd108 - (cos_val_s >>> 8);endelse if(cnt == 4'd5) beginwin_buf <= win_buf + ((16'sd82 * (cos_val_s >>> 7)) >>> 10);endelse beginwin_buf <= win_buf;endend// 4'd7: begin //凯塞窗// win_buf <= 16'sd0;// enddefault: beginwin_buf <= 16'sd256;endendcaseenddefault: beginwin_buf <= win_buf;endendcase
end//busy_buf
always @(*) begincase(state)S_IDLE: beginbusy_buf <= 1'b0;enddefault: beginbusy_buf <= 1'b1;endendcase
end//cos_phase
reg [15:0] k = 16'd0;
always @(posedge clk) begincase(state)S_CAL: begincase(win_type)4'd1: begin //矩形窗cos_phase <= 16'd0;end4'd2: begin //图基窗if(cnt == 4'd0) begink <= (n - 2'd2) / 4'd10;cos_phase <= cos_phase;endelse if(cnt == 4'd1) begink <= k;if(i <= k) begincos_phase <= i * (16'd32768 / (k + 1'b1)) + 16'd16384;endelse if(i > n - k - 2'd2) begincos_phase <= (n - i - 1'b1) * (16'd32768 / (k + 1'b1)) + 16'd16384;endelse begincos_phase <= 16'd0;endendelse begincos_phase <= cos_phase;k <= k;endend4'd3: begin //三角窗cos_phase <= 16'd0;end4'd4: begin //汉宁窗cos_phase <= 2'd2 * i * (16'd32768 / (n - 1'b1)) + 16'd16384;end4'd5: begin //海明窗cos_phase <= 2'd2 * i * (16'd32768 / (n - 1'b1)) + 16'd16384;end4'd6: begin //布莱克曼窗if(cnt == 4'd0) begincos_phase <= 2'd2 * i * (16'd32768 / (n - 1'b1)) + 16'd16384;endelse if(cnt == 4'd2) begincos_phase <= 4'd4 * i * (16'd32768 / (n - 1'b1)) + 16'd16384;endelse begincos_phase <= cos_phase;endend// 4'd7: begin //凯塞窗// cos_phase <= 16'd0;// enddefault: begincos_phase <= 16'd0;endendcaseenddefault: begincos_phase <= cos_phase;endendcase
end//sin_rom
reg [15:0] cos_phase = 16'd0;
wire [15:0] cos_out;
sin_gen sin_gen_inst(.clk (clk),.phase (cos_phase), //相位，0~65535对应[0~2pi).sin_out (cos_out) //0~65535
);wire signed [15:0] cos_val_s;
assign cos_val_s = {~cos_out[15], cos_out[14:0]};//win_buf_d0
always @(posedge clk) begincase(state)S_END: beginwin_buf_d0 <= win_buf;enddefault: beginwin_buf_d0 <= win_buf_d0;endendcase
end//------------------func------------------------------
function signed [15:0] abs(input signed [15:0] a);beginabs = (a >= 16'sd0)? a : -a;end
endfunctionendmodule
测试
testbench 如下
`timescale 1ns/100psmodule FIR_windows_generate_tb();reg clk_100M = 1'b1;
always #5 beginclk_100M <= ~clk_100M;
endreg rst_n = 1'b1;reg en; //上升沿触发窗口计算
reg [3:0] win_type; //窗口类型，1:矩形窗，2:图基窗，3:三角窗，4:汉宁窗，5:海明窗，6:布莱克曼窗
reg [15:0] n; //滤波器阶数
reg [15:0] i; //窗口索引值，0 ~ n-1wire busy;
wire signed [15:0] win;FIR_windows_generator FIR_windows_generator_inst(.clk (clk_100M),.rst_n (rst_n),.en (en), //上升沿触发窗口计算.win_type (win_type), //窗口类型，1:矩形窗，2:图基窗，3:三角窗，4:汉宁窗，5:海明窗，6:布莱克曼窗.n (n), //滤波器阶数.i (i), //窗口索引值，0 ~ n-1.busy (busy), //指示模块是否计算完成.win (win)
);//进行一组FIR_win的计算
task cal_win;input [3:0] WIN_TYPE;input [15:0] N;integer k;beginn = N;win_type = WIN_TYPE;#10;for (k = 0; k < N; k = k + 1'b1) begini = k;en = 1'b1;wait(busy);#10;en = 1'b0;wait(~busy);#10;endend
endtaskinitial beginrst_n <= 1'b0;en <= 1'b0;win_type <= 1'b1;n <= 16'd16;i <= 16'd0;#100;rst_n <= 1'b1;#100;cal_win(1, 64); //矩形窗#100;cal_win(3, 64); //三角窗#100;cal_win(2, 64); //图基窗#100;cal_win(4, 64); //汉宁窗#100;cal_win(5, 64); //海明窗#100;cal_win(6, 64); //布莱克曼窗#200;$stop;
endendmodule
仿真结果如下
滤波器系数计算
FIR 滤波器冲激响应
这里给出理想低通 FIR 滤波器，理想高通 FIR 滤波器、理想带通 FIR 滤波器、理想带阻 FIR 滤波器的冲激响应函数表达式：
- 低通
h L P ( n ) = sin ( 2 π f c f s s ) π s , where s = ∣ n − N 2 ∣ , n = 0 , 1 , . . . , N h_{LP}(n)=\frac{\sin(\frac{2\pi f_{c}}{f_s}s)}{\pi s},\ \text{where}\ s=|n-\frac{N}{2}|,\ n=0,1,...,N hLP(n)=πssin(fs2πfcs), where s=∣n−2N∣, n=0,1,...,N
其中 f s f_s fs 为采样率， f c f_c fc 为截止频率。
- 高通
h H P ( n ) = sin ( π s ) − sin ( 2 π f c f s s ) π s , where s = ∣ n − N 2 ∣ , n = 0 , 1 , . . . , N h_{HP}(n)=\frac{\sin(\pi s)-\sin(\frac{2\pi f_{c}}{f_s}s)}{\pi s},\ \text{where}\ s=|n-\frac{N}{2}|,\ n=0,1,...,N hHP(n)=πssin(πs)−sin(fs2πfcs), where s=∣n−2N∣, n=0,1,...,N
- 带通
h B P ( n ) = sin ( 2 π f c 2 f s s ) − sin ( 2 π f c 1 f s s ) π s , where s = ∣ n − N 2 ∣ , n = 0 , 1 , . . . , N h_{BP}(n)=\frac{\sin(\frac{2\pi f_{c2}}{f_s}s)-\sin(\frac{2\pi f_{c1}}{f_s}s)}{\pi s},\ \text{where}\ s=|n-\frac{N}{2}|,\ n=0,1,...,N hBP(n)=πssin(fs2πfc2s)−sin(fs2πfc1s), where s=∣n−2N∣, n=0,1,...,N
其中 f c 1 f_{c1} fc1 为下截止频率， f c 2 f_{c2} fc2 为上截止频率。
- 带阻
h B S ( n ) = sin ( 2 π f c 1 f s s ) + sin ( π s ) − sin ( 2 π f c 2 f s s ) π s , where s = ∣ n − N 2 ∣ , n = 0 , 1 , . . . , N h_{BS}(n)=\frac{\sin(\frac{2\pi f_{c1}}{f_s}s)+\sin(\pi s)-\sin(\frac{2\pi f_{c2}}{f_s}s)}{\pi s},\ \text{where}\ s=|n-\frac{N}{2}|,\ n=0,1,...,N hBS(n)=πssin(fs2πfc1s)+sin(πs)−sin(fs2πfc2s), where s=∣n−2N∣, n=0,1,...,N
在实际设计中，FIR 滤波的数据要加窗以将无限冲激的 sinc 函数截断为有限长（即窗函数法 FIR 滤波器设计），因此将以上冲激响应与窗函数相乘即可。在计算以上冲激函数时，当阶数 N 为偶数时，则会在 n = N / 2 n=N/2 n=N/2 时出现除零的问题，此时利用洛必达法则进行计算即可。
verilog 实现
/* * file : FIR_firwin_generator.v* author : 今朝无言* lab : WHU-EIS-LMSWE* date : 2024-09-26* version : v1.0* description : 生成指定阶数、指定类型的FIR滤波窗口*/
`default_nettype none
module FIR_firwin_generator(
input wire clk,
input wire rst_n,input wire en, //上升沿触发窗口计算
input wire [1:0] band_type, //滤波器类型，0:低通LP，1:高通HP，2:带通BP，3:带阻BS
input wire signed [15:0] fs, //采样率，注意fln,fhn均应小于fs/2
input wire signed [15:0] fln, //滤波器下频点，LP,HP,BP,BS均会用到
input wire signed [15:0] fhn, //滤波器上频点，BP,BS用到
input wire [3:0] win_type, //窗函数类型，1:矩形窗，2:图基窗Tukey，3:三角窗，4:汉宁窗Hann，5:海明窗Hamming，6:布莱克曼窗Blackman
input wire signed [15:0] n, //滤波器阶数 注意，HP/BS的阶数应为偶数，奇数阶的系数不可靠
input wire signed [15:0] i, //0~n，共n+1个值output wire busy, //指示模块是否计算完成
output wire signed [15:0] firwin
);reg signed [31:0] firwin_buf = 32'sd256;
reg signed [15:0] firwin_buf_d0 = 16'sd256; //8-8有符号定点数
reg busy_buf = 1'b0;assign firwin = firwin_buf_d0;
assign busy = busy_buf;localparam S_IDLE = 4'h1;
localparam S_CAL = 4'h2;
localparam S_END = 4'h4;reg [3:0] state = S_IDLE;
reg [3:0] next_state;always @(posedge clk) beginif(~rst_n) beginstate <= S_IDLE;endelse beginstate <= next_state;end
endalways @(*) begincase(state)S_IDLE: beginif(en_pe) beginnext_state <= S_CAL;endelse beginnext_state <= S_IDLE;endendS_CAL: beginif(cnt >= 4'd12) begin //最迟在cnt=7可以读取窗函数值并计算firwin，随后本模块可计算firwinnext_state <= S_END;endelse beginnext_state <= S_CAL;endendS_END: beginnext_state <= S_IDLE;enddefault: beginnext_state <= S_IDLE;endendcase
end//firwin_buf
always @(posedge clk) begincase(state)S_CAL: begincase(band_type)2'd0: begin //LPif(cnt == 4'd3) beginif((~n[0]) && (i_buf == n/4'sd2)) begin //偶数阶滤波器，计算最中间的滤波器系数 即洛必达求=0时的值firwin_buf <= (({fln, 16'b0} / fs) * 16'sd804) >>> 8; //3.1415 = 804/256endelse beginfirwin_buf <= sin_val_s / s_mlti2 * 4'sd2;endendelse if(cnt == 4'd7) beginfirwin_buf <= (firwin_buf * win) >>> 16;endelse beginfirwin_buf <= firwin_buf;endend2'd1: begin //HPif(cnt == 4'd3) beginif((~n[0]) && (i_buf == n/4'sd2)) begin //偶数阶滤波器，计算最中间的滤波器系数 即洛必达求=0时的值firwin_buf <= ((32'sd32768 - {fln, 16'b0} / fs) * 16'sd804) >>> 8;endelse beginfirwin_buf <= sin_val_s;endendelse if(cnt == 4'd7) beginif((~n[0]) && (i_buf == n/4'sd2)) beginfirwin_buf <= firwin_buf;endelse beginfirwin_buf <= (firwin_buf - sin_val_s) / s_mlti2 * 4'sd2;endendelse if(cnt == 4'd8) beginfirwin_buf <= (firwin_buf * win) >>> 16;endelse beginfirwin_buf <= firwin_buf;endend2'd2: begin //BPif(cnt == 4'd3) beginif((~n[0]) && (i_buf == n/4'sd2)) begin //偶数阶滤波器，计算最中间的滤波器系数 即洛必达求=0时的值firwin_buf <= ((({fhn, 16'b0} - {fln, 16'b0}) / fs) * 16'sd804) >>> 8;endelse beginfirwin_buf <= sin_val_s;endendelse if(cnt == 4'd7) beginif((~n[0]) && (i_buf == n/4'sd2)) beginfirwin_buf <= firwin_buf;endelse beginfirwin_buf <= (firwin_buf - sin_val_s) / s_mlti2 * 4'sd2;endendelse if(cnt == 4'd8) beginfirwin_buf <= (firwin_buf * win) >>> 16;endelse beginfirwin_buf <= firwin_buf;endend2'd3: begin //BSif(cnt == 4'd3) beginif((~n[0]) && (i_buf == n/4'sd2)) begin //偶数阶滤波器，计算最中间的滤波器系数 即洛必达求=0时的值firwin_buf <= (({fln, 16'b0} / fs + 32'sd32768 - {fhn, 16'b0} / fs) * 16'sd804) >>> 8;endelse beginfirwin_buf <= sin_val_s;endendelse if(cnt == 4'd7) beginif((~n[0]) && (i_buf == n/4'sd2)) beginfirwin_buf <= firwin_buf;endelse beginfirwin_buf <= firwin_buf + sin_val_s;endendelse if(cnt == 4'd11) beginif((~n[0]) && (i_buf == n/4'sd2)) beginfirwin_buf <= firwin_buf;endelse beginfirwin_buf <= (firwin_buf - sin_val_s) / s_mlti2 * 4'sd2;endendelse if(cnt == 4'd12) beginfirwin_buf <= (firwin_buf * win) >>> 16;endelse beginfirwin_buf <= firwin_buf;endenddefault: beginfirwin_buf <= firwin_buf;endendcaseenddefault: beginfirwin_buf <= firwin_buf;endendcase
end//i_buf
reg signed [15:0] i_buf;
always @(posedge clk) beginif(i > (n >>> 1)) begini_buf <= n - i; //滤波器是对称的，这里处理后利用i_buf计算滤波器系数endelse begini_buf <= i;end
end//sin_phase
reg [31:0] multi_tmp;
always @(posedge clk) begincase(state)S_CAL: beginsin_phase <= multi_tmp[15:0];enddefault: beginsin_phase <= sin_phase;endendcase
endreg signed [15:0] s_mlti2;
always @(*) begins_mlti2 <= n - i_buf * 4'sd2;
endalways @(*) begincase(state)S_CAL: begincase(band_type)2'd0: begin //LPmulti_tmp <= (({fln, 16'b0} / fs) * s_mlti2) >> 1;end2'd1: begin //HPif(cnt <= 4'd3) beginmulti_tmp <= {s_mlti2, 14'b0};endelse beginmulti_tmp <= (({fln, 16'b0} / fs) * s_mlti2) >> 1;endend2'd2: begin //BPif(cnt <= 4'd3) beginmulti_tmp <= (({fhn, 16'b0} / fs) * s_mlti2) >> 1;endelse beginmulti_tmp <= (({fln, 16'b0} / fs) * s_mlti2) >> 1;endend2'd3: begin //BSif(cnt <= 4'd3) beginmulti_tmp <= (({fln, 16'b0} / fs) * s_mlti2) >> 1;endelse if(cnt <= 4'd7) beginmulti_tmp <= {s_mlti2, 14'b0};endelse beginmulti_tmp <= (({fhn, 16'b0} / fs) * s_mlti2) >> 1;endenddefault: beginmulti_tmp <= 32'd0;endendcaseenddefault: beginmulti_tmp <= 32'd0;endendcase
end//窗函数
wire signed [15:0] win;
FIR_windows_generator FIR_windows_generator_inst(.clk (clk),.rst_n (rst_n),.en (en), //上升沿触发窗口计算.win_type (win_type), //窗口类型，1:矩形窗，2:图基窗Tukey，3:三角窗，4:汉宁窗Hann，5:海明窗Hamming，6:布莱克曼窗Blackman.n (n + 1'b1), //窗口长度，=滤波器阶数+1.i (i), //窗口索引值.busy (), //指示模块是否计算完成.win (win)
);//en 边沿检测
wire en_pe;
detect_sig_edge detect_sig_edge_inst(.clk (clk), //工作时钟.sig (en), //待检测信号.sig_pe (en_pe), //信号上升沿.sig_ne (), //下降沿.sig_de () //双边沿
);//cnt 控制计算流程
reg [3:0] cnt = 4'd0;
always @(posedge clk) begincase(state)S_IDLE: begincnt <= 4'd0;endS_CAL: begincnt <= cnt + 1'b1;enddefault: begincnt <= 4'd0;endendcase
end//busy_buf
always @(*) begincase(state)S_IDLE: beginbusy_buf <= 1'b0;enddefault: beginbusy_buf <= 1'b1;endendcase
end//sin_rom
reg [15:0] sin_phase = 16'd0;
wire [15:0] sin_out;
sin_gen sin_gen_inst(.clk (clk),.phase (sin_phase), //相位，0~65535对应[0~2pi).sin_out (sin_out) //0~65535
);wire signed [15:0] sin_val_s;
assign sin_val_s = {~sin_out[15], sin_out[14:0]};//firwin_buf_d0
always @(posedge clk) begincase(state)S_END: beginfirwin_buf_d0 <= firwin_buf[15:0];enddefault: beginfirwin_buf_d0 <= firwin_buf_d0;endendcase
endendmodule
测试
testbench 如下
`timescale 1ns/100psmodule FIR_firwin_generate_tb();reg clk_100M = 1'b1;
always #5 beginclk_100M <= ~clk_100M;
endreg rst_n = 1'b1;reg en; //上升沿触发窗口计算reg [1:0] band_type; //滤波器类型，0:低通LP，1:高通HP，2:带通BP，3:带阻BS
reg [15:0] fs; //采样率，注意fln,fhn均应小于fs/2
reg [15:0] fln; //滤波器下频点，LP,HP,BP,BS均会用到
reg [15:0] fhn; //滤波器上频点，BP,BS用到
reg [3:0] win_type; //窗口类型，1:矩形窗，2:图基窗，3:三角窗，4:汉宁窗，5:海明窗，6:布莱克曼窗
reg [15:0] n; //滤波器阶数
reg [15:0] i; //窗口索引值，0 ~ nwire busy;
wire signed [15:0] firwin;FIR_firwin_generator FIR_firwin_generator_inst(.clk (clk_100M),.rst_n (rst_n),.en (en), //上升沿触发窗口计算.band_type (band_type), //滤波器类型，0:低通LP，1:高通HP，2:带通BP，3:带阻BS.fs (fs), //采样率，注意fln,fhn均应小于fs/2.fln (fln), //滤波器下频点，LP,HP,BP,BS均会用到.fhn (fhn), //滤波器上频点，BP,BS用到.win_type (win_type), //窗函数类型，1:矩形窗，2:图基窗Tukey，3:三角窗，4:汉宁窗Hann，5:海明窗Hamming，6:布莱克曼窗Blackman.n (n), //滤波器阶数.i (i), //0~n，共n+1个值.busy (busy),.firwin (firwin)
);//进行一组FIR_win的计算
task cal_firwin;input [1:0] BAND_TYPE;input [15:0] Fs;input [15:0] Fln;input [15:0] Fhn;input [3:0] WIN_TYPE;input [15:0] N;integer k;beginband_type = BAND_TYPE;fs = Fs;fln = Fln;fhn = Fhn;win_type = WIN_TYPE;n = N;#10;for (k = 0; k <= N; k = k + 1'b1) begini = k;en = 1'b1;wait(busy);#10;en = 1'b0;wait(~busy);#10;endend
endtaskinitial beginrst_n <= 1'b0;en <= 1'b0;band_type <= 2'd0;fs <= 16'd100;fln <= 16'd10;fhn <= 16'd60;win_type <= 4'd1;n <= 16'd64;i <= 16'd0;#100;rst_n <= 1'b1;#100;//可与matlab函数fir1(fir_N, Wn, band_type, win)的结果比对 注意其中的Wn是 [fln/f_ny, fhn/f_ny]，其中f_ny=fs/2cal_firwin(2'd0, 16'd1000, 16'd50, 16'd100, 4'd1, 16'd64); //LP，矩形窗#200;cal_firwin(2'd0, 16'd1000, 16'd50, 16'd100, 4'd5, 16'd64); //LP，海明窗#200;cal_firwin(2'd0, 16'd1000, 16'd50, 16'd100, 4'd6, 16'd64); //LP，布莱克曼窗#200;cal_firwin(2'd0, 16'd1000, 16'd50, 16'd100, 4'd6, 16'd63); //LP，布莱克曼窗#200;cal_firwin(2'd1, 16'd1000, 16'd50, 16'd100, 4'd1, 16'd64); //HP，矩形窗#200;cal_firwin(2'd1, 16'd1000, 16'd50, 16'd100, 4'd1, 16'd63); //HP，矩形窗 HP的阶数应为偶数，否则系数不可靠，matlab fir1也是只能生成偶数阶的HP#200;cal_firwin(2'd2, 16'd1000, 16'd50, 16'd100, 4'd1, 16'd64); //BP，矩形窗#200;cal_firwin(2'd2, 16'd1000, 16'd50, 16'd100, 4'd1, 16'd63); //BP，矩形窗#200;cal_firwin(2'd2, 16'd1000, 16'd50, 16'd100, 4'd5, 16'd63); //BP，海明窗#200;cal_firwin(2'd3, 16'd1000, 16'd50, 16'd100, 4'd1, 16'd64); //BS，矩形窗#200;cal_firwin(2'd3, 16'd1000, 16'd50, 16'd100, 4'd1, 16'd63); //BS，矩形窗 BS的阶数也应为偶数#200;cal_firwin(2'd3, 16'd1000, 16'd50, 16'd100, 4'd5, 16'd64); //BS，海明窗#200;#200;$stop;
endendmodule
仿真结果如下
读者可与 Matlab 的 fir1 函数结果进行比对。
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