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--- fpga滤波器实现 [2020/07/22 14:28]
zili
+++ — (当前版本)
@@ 行 1: / 行 1: @@
-### FPGA滤波器实现
-\\
-#### FPGA滤波器实施概述
-我协助我的一位研究生进行了一些有关FPGA滤波器实现的定向研究。她的任务是了解并实现FPGA硬件上的几种类型的过滤器。设计的所有滤波器均为15阶滤波器，并使用16位定点数学运算。然后检查了过滤器的性能和资源使用情况。她关于研究的最终演讲可以在下面查看：\\
-[[https://www.eetree.cn/wiki/_media/filter_implementation_on_a_fpga_board_xueyan_lu_06152017.pdf|FPGA滤波器实现]]\\
-研究项目期间创建的Verilog源文件如下。\\
-\\
-#### FIR滤波器
-FIR滤波器是四个滤波器中最简单，最快的。它利用了预加器的对称性。而且，使用加法器树来最小化组合路径延迟。\\
-{{ ::fir_filter.png |}}
-##### FIR_Filter.v
-<code verilog>
-`define FILT_LENGTH 16
-module FIR_Filter(
-    input  clk,
-    input  en,
-    input  [15:0]din,
-    output [15:0]dout
-    );
-    reg signed [15:0]coeff[`FILT_LENGTH/2-1:0]; //Filter coefficients.
-    reg signed [15:0]delay_line[`FILT_LENGTH-1:0]; //Input delay line.
-    wire [31:0]accum; //Accumulator for output filter calculation.
-    integer i; //Initialization integer.
-    genvar c;  //Delay line generation variable.
-    reg signed [16:0]preadd_regs[7:0]; //Save calc after preadd.
-    reg signed [31:0]mult_regs[7:0];   //Save calc after multiplication.
-    reg signed [31:0]tree1_regs[3:0];  //Save calc after first layer of adder tree.
-    reg signed [31:0]tree2_regs[1:0];  //Save calc after first layer of adder tree.
-    reg signed [31:0]treeout_reg;      //Save calc after complete.
-    //assign dout = treeout_reg[31:16];
-    //Calculate value in the accumulator.
-    assign accum = (delay_line[0] + delay_line[15]) * coeff[0] +
-                   (delay_line[1] + delay_line[14]) * coeff[1] +
-                   (delay_line[2] + delay_line[13]) * coeff[2] +
-                   (delay_line[3] + delay_line[12]) * coeff[3] +
-                   (delay_line[4] + delay_line[11]) * coeff[4] +
-                   (delay_line[5] + delay_line[10]) * coeff[5] +
-                   (delay_line[6] + delay_line[9])  * coeff[6] +
-                   (delay_line[7] + delay_line[8])  * coeff[7];
-    //Assign upper 16-bits to output.
-    assign dout = accum[31:16];
-    initial begin
-        //Load the filter coefficients.
-        coeff[0] = 16'd2320;
-        coeff[1] = 16'd4143;
-        coeff[2] = 16'd4592;
-        coeff[3] = 16'd7278;
-        coeff[4] = 16'd8423;
-        coeff[5] = 16'd10389;
-        coeff[6] = 16'd11269;
-        coeff[7] = 16'd12000;
-        //Initialize delay line.
-        for(i = 0; i < `FILT_LENGTH; i = i+1'b1) begin
-            delay_line[i] = 16'd0;
-        end
-        //Initialize the preadder regs.
-        for(i = 0; i < 8; i = i+1'b1) begin
-            preadd_regs[i] = 17'd0;
-        end
-        //Initialize the multiplier regs.
-        for(i = 0; i < 8; i = i+1'b1) begin
-            mult_regs[i] = 32'd0;
-        end
-        //Initialize the first layer of the adder tree regs.
-        for(i = 0; i < 4; i = i+1'b1) begin
-            tree1_regs[i] = 32'd0;
-        end
-        //Initialize the second layer of the adder tree regs.
-        for(i = 0; i < 2; i = i+1'b1) begin
-            tree2_regs[i] = 32'd0;
-        end
-        //Initialize the adder tree output reg.
-        treeout_reg = 32'd0;
-    end
-    //Advance the data through the delay line every clock cycle.
-    generate
-        for (c = `FILT_LENGTH-1; c > 0; c = c - 1) begin: inc_delay
-            always @(posedge clk) begin
-                if(en) delay_line[c] <= delay_line[c-1];
-            end
-        end
-    endgenerate
-    //Update with input data.
-    always @(posedge clk) begin
-        if(en) delay_line[0] <= din;
-    end
-endmodule
-</code>
-\\
-##### filter_top.v
-<code verilog>
-module filter_top(
-    input clk,
-    input [7:0]sw,
-    output [7:0]JA
-    );
-    wire [15:0]tout; //The output of the tone lookup table.
-    wire [15:0]fout; //The output of the FIR filter.
-    wire [15:0]mout; //Selected output.
-    wire en;         //Clock enble.
-    wire clk_out;    //264MHz System clock.
-    assign en = 1'b1;
-    clk_wiz_0 cw (.clk_in1(clk), .clk_out1(clk_out));
-    //clk_en ce(.clk(clk_out), .en(en));
-    ToneGen tg(.clk(clk_out), .en(en), .dout(tout));
-    FIR_Filter ff(.clk(clk_out), .en(en), .din(tout), .dout(fout));
-    //Choose filtered or unfiltered output based on sw0.
-    assign mout = sw[0] ? fout : tout;
-    //Take only the upper 8 bits and make it unsigned.
-    //assign JA = mout[15:8] + 8'd128;
-    assign {JA[3:0], JA[7:4]} = mout[15:8] + 8'd128;
-endmodule
-</code>
-\\
-##### ToneGen.v
-<code verilog>
-`timescale 1ns/1ps
-module ToneGen(
-    input clk,
-    input en,
-    output [15:0]dout
-    );
-    //Tone generation data.  At a 44KHz sampling rate, the lookup table
-    //generates a 440Hz and 4.4KHz tone mixed together.
-    reg [15:0]tonetbl[99:0];
-    //Pointer into the tone table.
-    reg [6:0]toneptr = 7'h00;
-    initial begin
-        tonetbl[0] = 10970;
-        tonetbl[1] = 18151;
-        tonetbl[2] = 19197;
-        tonetbl[3] = 14105;
-        tonetbl[4] = 5211;
-        tonetbl[5] = -3704;
-        tonetbl[6] = -8858;
-        tonetbl[7] = -7914;
-        tonetbl[8] = -876;
-        tonetbl[9] = 9912;
-        tonetbl[10] = 20660;
-        tonetbl[11] = 27581;
-        tonetbl[12] = 28330;
-        tonetbl[13] = 22905;
-        tonetbl[14] = 13642;
-        tonetbl[15] = 4326;
-        tonetbl[16] = -1260;
-        tonetbl[17] = -780;
-        tonetbl[18] = 5767;
-        tonetbl[19] = 16037;
-        tonetbl[20] = 26244;
-        tonetbl[21] = 32601;
-        tonetbl[22] = 32767;
-        tonetbl[23] = 26741;
-        tonetbl[24] = 16863;
-        tonetbl[25] = 6918;
-        tonetbl[26] = 692;
-        tonetbl[27] = 527;
-        tonetbl[28] = 6421;
-        tonetbl[29] = 16037;
-        tonetbl[30] = 25590;
-        tonetbl[31] = 31295;
-        tonetbl[32] = 30814;
-        tonetbl[33] = 24149;
-        tonetbl[34] = 13642;
-        tonetbl[35] = 3081;
-        tonetbl[36] = -3745;
-        tonetbl[37] = -4494;
-        tonetbl[38] = 837;
-        tonetbl[39] = 9912;
-        tonetbl[40] = 18947;
-        tonetbl[41] = 24161;
-        tonetbl[42] = 23217;
-        tonetbl[43] = 16119;
-        tonetbl[44] = 5211;
-        tonetbl[45] = -5718;
-        tonetbl[46] = -12878;
-        tonetbl[47] = -13924;
-        tonetbl[48] = -8853;
-        tonetbl[49] = 0;
-        tonetbl[50] = 8853;
-        tonetbl[51] = 13924;
-        tonetbl[52] = 12878;
-        tonetbl[53] = 5718;
-        tonetbl[54] = -5211;
-        tonetbl[55] = -16119;
-        tonetbl[56] = -23217;
-        tonetbl[57] = -24161;
-        tonetbl[58] = -18947;
-        tonetbl[59] = -9912;
-        tonetbl[60] = -837;
-        tonetbl[61] = 4494;
-        tonetbl[62] = 3745;
-        tonetbl[63] = -3081;
-        tonetbl[64] = -13642;
-        tonetbl[65] = -24149;
-        tonetbl[66] = -30814;
-        tonetbl[67] = -31295;
-        tonetbl[68] = -25590;
-        tonetbl[69] = -16037;
-        tonetbl[70] = -6421;
-        tonetbl[71] = -527;
-        tonetbl[72] = -692;
-        tonetbl[73] = -6918;
-        tonetbl[74] = -16863;
-        tonetbl[75] = -26741;
-        tonetbl[76] = -32767;
-        tonetbl[77] = -32601;
-        tonetbl[78] = -26244;
-        tonetbl[79] = -16037;
-        tonetbl[80] = -5767;
-        tonetbl[81] = 780;
-        tonetbl[82] = 1260;
-        tonetbl[83] = -4326;
-        tonetbl[84] = -13642;
-        tonetbl[85] = -22905;
-        tonetbl[86] = -28330;
-        tonetbl[87] = -27581;
-        tonetbl[88] = -20660;
-        tonetbl[89] = -9912;
-        tonetbl[90] = 876;
-        tonetbl[91] = 7914;
-        tonetbl[92] = 8858;
-        tonetbl[93] = 3704;
-        tonetbl[94] = -5211;
-        tonetbl[95] = -14105;
-        tonetbl[96] = -19197;
-        tonetbl[97] = -18151;
-        tonetbl[98] = -10970;
-        tonetbl[99] = 0;
-    end
-    //Assign the output to the value in the lookup table
-    //pointed to by toneptr.
-    assign dout = tonetbl[toneptr];
-    //Increment through the tone lookup table and wrap back
-    //to zero when at the end.
-    always @(posedge clk) begin
-        if(en) begin
-            if(toneptr == 7'd99) begin
-                toneptr <= 7'd0;
-            end
-            else begin
-                toneptr <= toneptr + 1'b1;
-            end
-        end
-    end
-endmodule
-</code>
-\\
-##### clk_en.v
-<code verilog>
-module clk_en(
-    input clk,
-    output reg en = 1'b0
-    );
-    reg [15:0]en_counter = 16'h0;
-    always @(posedge clk) begin
-        if(en_counter == 16'd5999) begin
-            en_counter <= 16'h0;
-            en <= 1'b1;
-        end
-        else begin
-            en_counter <= en_counter + 1'b1;
-            en <= 1'b0;
-        end
-    end
-endmodule
-</code>
-\\
-##### TB_ToneGen.v
-<code verilog>
-module TB_ToneGen;
-    reg clk = 1'b0;
-    reg sw0 = 1'b1;
-    wire [7:0]JA;
-    wire en;
-    //wire [15:0]cout;
-    filter_top uut(.clk(clk), .sw({15'h00,sw0}), .JA({JA[3:0], JA[7:4]}));
-    assign en = uut.en;
-    //assign cout = uut.ce.en_counter;
-    //initial begin
-    //     #600000 sw0 = 1'b1;
-    //end
-    //100MHz clock
-    always #5 clk = ~clk;
-endmodule
-</code>
-\\
-\\
-#### LMS自适应滤波器
-LMS自适应滤波器在单个时钟周期内完成其输出计算和权重更新。由于其单周期运行，因此存在大量的组合延迟。该滤波器只能以FIR滤波器速度的一小部分运行。\\
-{{ ::lms_adaptive_filter.png |}}
-##### LMS_Adapt.v
-<code verilog>
-`define ADAPT_FILT_LENGTH 16
-module LMS_Adapt(
-    input  clk,
-    input  en,
-    input  [15:0]din,
-    input  signed [15:0]desired,
-    output signed [15:0]dout,
-    output signed [15:0]err
-    );
-    parameter MU = 16'd32767;
-    reg  signed [15:0]mu = MU;
-    reg  signed [15:0]coeff[`ADAPT_FILT_LENGTH-1:0]; //Filter coefficients.
-    reg  signed [15:0]delay_line[`ADAPT_FILT_LENGTH-1:0]; //Input delay line.
-    wire signed [31:0]accum; //Accumulator for output filter calculation.
-    wire signed [31:0]stepped; //Error after step sized applied.
-    integer i; //Initialization integer.
-    genvar c;  //Delay line generation variable.
-    //Calculate the error and multiply it by the step size.
-    assign err = desired - dout;
-    //assign stepped = err * mu;
-    assign stepped = err << 15;
-    //Calculate value in the accumulator.
-    assign accum = delay_line[0]*coeff[0] +
-                   delay_line[1]*coeff[1] +
-                   delay_line[2]*coeff[2] +
-                   delay_line[3]*coeff[3] +
-                   delay_line[4]*coeff[4] +
-                   delay_line[5]*coeff[5] +
-                   delay_line[6]*coeff[6] +
-                   delay_line[7]*coeff[7] +
-                   delay_line[8]*coeff[8] +
-                   delay_line[9]*coeff[9] +
-                   delay_line[10]*coeff[10] +
-                   delay_line[11]*coeff[11] +
-                   delay_line[12]*coeff[12] +
-                   delay_line[13]*coeff[13] +
-                   delay_line[14]*coeff[14] +
-                   delay_line[15]*coeff[15];
-    //Assign upper 16-bits to output.
-    assign dout = accum[31:16];
-    initial begin
-        //Load the filter coefficients.
-        coeff[0]  = 20'd0;
-        coeff[1]  = 20'd0;
-        coeff[2]  = 20'd0;
-        coeff[3]  = 20'd0;
-        coeff[4]  = 20'd0;
-        coeff[5]  = 20'd0;
-        coeff[6]  = 20'd0;
-        coeff[7]  = 20'd0;
-        coeff[8]  = 20'd0;
-        coeff[9]  = 20'd0;
-        coeff[10] = 20'd0;
-        coeff[11] = 20'd0;
-        coeff[12] = 20'd0;
-        coeff[13] = 20'd0;
-        coeff[14] = 20'd0;
-        coeff[15] = 20'd0;
-        //Initialize delay line.
-        for(i = 0; i < `ADAPT_FILT_LENGTH; i = i+1'b1) begin
-            delay_line[i] = 16'd0;
-        end
-    end
-    //Advance the data through the delay line every clock cycle.
-    generate
-        for (c = `ADAPT_FILT_LENGTH-1; c > 0; c = c - 1) begin: inc_delay
-            always @(posedge clk) begin
-                if(en) delay_line[c] <= delay_line[c-1];
-            end
-        end
-    endgenerate
-    //Update with input data.
-    always @(posedge clk) begin
-        if(en) delay_line[0] <= din;
-    end
-    wire signed [31:0]num2[`ADAPT_FILT_LENGTH-1:0];
-    wire signed [15:0]n1[`ADAPT_FILT_LENGTH-1:0];
-    wire signed [15:0]n2[`ADAPT_FILT_LENGTH-1:0];
-    //Update the coefficients with the LMS algorithm.
-    generate
-        for (c = `ADAPT_FILT_LENGTH; c > 0; c = c - 1) begin: adapt_update
-            assign n1[c-1] = stepped[31:16];
-            assign num2[c-1] = n1[c-1]*delay_line[c-1];
-            assign n2[c-1] = num2[c-1][31:16];
-            always @(posedge clk) begin
-                if(en) coeff[c-1] <= coeff[c-1] + n2[c-1];
-            end
-        end
-    endgenerate
-endmodule
-</code>
-\\
-##### filter_top.v
-<code verilog>
-module filter_top(
-    input clk,
-    input [7:0]sw,
-    output [7:0]JA
-    );
-    wire signed [15:0]tout;           //Output of the tone lookup table.
-    wire [15:0]fout;                  //Output of the FIR filter.
-    wire [15:0]aout;                  //Output of the adaptive filter.
-    wire [15:0]err;                   //Adaptive filter error.
-    wire [15:0]lfsr_out;              //16-bit Random noise variable.
-    wire en;                          //Clock enble.
-    wire [9:0]rnd;                    //10-bit noise.
-    wire signed [15:0]tone_and_noise; //Combination of tone and noise.
-    wire signed [15:0]delay_out;      //Output of the delay line.
-    wire [15:0]mout;                  //Selected desired output.
-    wire clk19_8MHz;                  //19.8MHz system clock.
-    assign rnd = lfsr_out[15:6];
-    assign tone_and_noise = tout + rnd;
-    //assign en = 1'b1;
-    clk_wiz_0 cw(.clk_in1(clk), .clk_out1(clk19_8MHz), .reset(1'b0));
-    ToneGen tg(.clk(clk19_8MHz), .en(en), .dout(tout));
-    FIR_Filter ff(.clk(clk19_8MHz), .en(en), .din(tone_and_noise), .dout(fout));
-    LMS_Adapt af(.clk(clk19_8MHz), .en(en), .din(tone_and_noise), .desired(mout), .dout(aout), .err(err));
-    lfsr sr(.clk(clk19_8MHz), .en(en), .lfsr_out(lfsr_out));
-    clk_en ce(.clk(clk19_8MHz), .en(en));
-    //Choose filtered or unfiltered output based on sw0.
-    assign mout = sw[0] ? fout : tone_and_noise;//delay_out;
-    //Take only the upper 8 bits and make it unsigned.
-    assign {JA[3:0], JA[7:4]} = aout[15:8] + 8'd128;
-    //assign JA[7:0] = aout[15:8] + 8'd128;
-    //assign {JA[3:0], JA[7:4]} = sw[7:0];
-endmodule
-</code>
-\\
-##### ToneGen.v
-<code verilog>
-`timescale 1ns/1ps
-module ToneGen(
-    input clk,
-    input en,
-    output [15:0]dout
-    );
-    //Tone generation data.  At a 44KHz sampling rate, the lookup table
-    //generates a 440Hz and 4.4KHz tone mixed together.
-    reg [15:0]tonetbl[99:0];
-    //Pointer into the tone table.
-    reg [6:0]toneptr = 7'h00;
-    initial begin
-        tonetbl[0] = 10970;
-        tonetbl[1] = 18151;
-        tonetbl[2] = 19197;
-        tonetbl[3] = 14105;
-        tonetbl[4] = 5211;
-        tonetbl[5] = -3704;
-        tonetbl[6] = -8858;
-        tonetbl[7] = -7914;
-        tonetbl[8] = -876;
-        tonetbl[9] = 9912;
-        tonetbl[10] = 20660;
-        tonetbl[11] = 27581;
-        tonetbl[12] = 28330;
-        tonetbl[13] = 22905;
-        tonetbl[14] = 13642;
-        tonetbl[15] = 4326;
-        tonetbl[16] = -1260;
-        tonetbl[17] = -780;
-        tonetbl[18] = 5767;
-        tonetbl[19] = 16037;
-        tonetbl[20] = 26244;
-        tonetbl[21] = 32601;
-        tonetbl[22] = 32767;
-        tonetbl[23] = 26741;
-        tonetbl[24] = 16863;
-        tonetbl[25] = 6918;
-        tonetbl[26] = 692;
-        tonetbl[27] = 527;
-        tonetbl[28] = 6421;
-        tonetbl[29] = 16037;
-        tonetbl[30] = 25590;
-        tonetbl[31] = 31295;
-        tonetbl[32] = 30814;
-        tonetbl[33] = 24149;
-        tonetbl[34] = 13642;
-        tonetbl[35] = 3081;
-        tonetbl[36] = -3745;
-        tonetbl[37] = -4494;
-        tonetbl[38] = 837;
-        tonetbl[39] = 9912;
-        tonetbl[40] = 18947;
-        tonetbl[41] = 24161;
-        tonetbl[42] = 23217;
-        tonetbl[43] = 16119;
-        tonetbl[44] = 5211;
-        tonetbl[45] = -5718;
-        tonetbl[46] = -12878;
-        tonetbl[47] = -13924;
-        tonetbl[48] = -8853;
-        tonetbl[49] = 0;
-        tonetbl[50] = 8853;
-        tonetbl[51] = 13924;
-        tonetbl[52] = 12878;
-        tonetbl[53] = 5718;
-        tonetbl[54] = -5211;
-        tonetbl[55] = -16119;
-        tonetbl[56] = -23217;
-        tonetbl[57] = -24161;
-        tonetbl[58] = -18947;
-        tonetbl[59] = -9912;
-        tonetbl[60] = -837;
-        tonetbl[61] = 4494;
-        tonetbl[62] = 3745;
-        tonetbl[63] = -3081;
-        tonetbl[64] = -13642;
-        tonetbl[65] = -24149;
-        tonetbl[66] = -30814;
-        tonetbl[67] = -31295;
-        tonetbl[68] = -25590;
-        tonetbl[69] = -16037;
-        tonetbl[70] = -6421;
-        tonetbl[71] = -527;
-        tonetbl[72] = -692;
-        tonetbl[73] = -6918;
-        tonetbl[74] = -16863;
-        tonetbl[75] = -26741;
-        tonetbl[76] = -32767;
-        tonetbl[77] = -32601;
-        tonetbl[78] = -26244;
-        tonetbl[79] = -16037;
-        tonetbl[80] = -5767;
-        tonetbl[81] = 780;
-        tonetbl[82] = 1260;
-        tonetbl[83] = -4326;
-        tonetbl[84] = -13642;
-        tonetbl[85] = -22905;
-        tonetbl[86] = -28330;
-        tonetbl[87] = -27581;
-        tonetbl[88] = -20660;
-        tonetbl[89] = -9912;
-        tonetbl[90] = 876;
-        tonetbl[91] = 7914;
-        tonetbl[92] = 8858;
-        tonetbl[93] = 3704;
-        tonetbl[94] = -5211;
-        tonetbl[95] = -14105;
-        tonetbl[96] = -19197;
-        tonetbl[97] = -18151;
-        tonetbl[98] = -10970;
-        tonetbl[99] = 0;
-    end
-    //Assign the output to the value in the lookup table
-    //pointed to by toneptr.
-    assign dout = tonetbl[toneptr];
-    //Increment through the tone lookup table and wrap back
-    //to zero when at the end.
-    always @(posedge clk) begin
-        if(en) begin
-            if(toneptr == 7'd99) begin
-                toneptr <= 7'd0;
-            end
-            else begin
-                toneptr <= toneptr + 1'b1;
-            end
-        end
-    end
-endmodule
-</code>
-\\
-##### FIR_Filter.v
-<code verilog>
-`define FILT_LENGTH 16
-module FIR_Filter(
-    input  clk,
-    input  en,
-    input  [15:0]din,
-    output [15:0]dout
-    );
-    reg signed [15:0]coeff[`FILT_LENGTH/2-1:0]; //Filter coefficients.
-    reg signed [15:0]delay_line[`FILT_LENGTH-1:0]; //Input delay line.
-    wire [31:0]accum; //Accumulator for output filter calculation.
-    integer i; //Initialization integer.
-    genvar c;  //Delay line generation variable.
-    //Calculate value in the accumulator.
-    assign accum = (delay_line[0] + delay_line[15]) * coeff[0] +
-                   (delay_line[1] + delay_line[14]) * coeff[1] +
-                   (delay_line[2] + delay_line[13]) * coeff[2] +
-                   (delay_line[3] + delay_line[12]) * coeff[3] +
-                   (delay_line[4] + delay_line[11]) * coeff[4] +
-                   (delay_line[5] + delay_line[10]) * coeff[5] +
-                   (delay_line[6] + delay_line[9])  * coeff[6] +
-                   (delay_line[7] + delay_line[8])  * coeff[7];
-    //Assign upper 16-bits to output.
-    assign dout = accum[31:16];
-    initial begin
-        //Load the filter coefficients.
-        coeff[0] = 16'd2552;
-        coeff[1] = 16'd4557;
-        coeff[2] = 16'd5051;
-        coeff[3] = 16'd8006;
-        coeff[4] = 16'd9265;
-        coeff[5] = 16'd11427;
-        coeff[6] = 16'd12396;
-        coeff[7] = 16'd13200;
-        //Initialize delay line.
-        for(i = 0; i < `FILT_LENGTH; i = i+1'b1) begin
-            delay_line[i] = 16'd0;
-        end
-    end
-    //Advance the data through the delay line every clock cycle.
-    generate
-        for (c = `FILT_LENGTH-1; c > 0; c = c - 1) begin: inc_delay
-            always @(posedge clk) begin
-                if(en) delay_line[c] <= delay_line[c-1];
-            end
-        end
-    endgenerate
-    //Update with input data.
-    always @(posedge clk) begin
-        if(en) delay_line[0] <= din;
-    end
-endmodule
-</code>
-\\
-##### clk_en.v
-<code verilog>
-module clk_en(
-    input clk,
-    output reg en = 1'b0
-    );
-    reg [15:0]en_counter = 16'h0;
-    always @(posedge clk) begin
-        if(en_counter == 16'd449) begin
-            en_counter <= 16'h0;
-            en <= 1'b1;
-        end
-        else begin
-            en_counter <= en_counter + 1'b1;
-            en <= 1'b0;
-        end
-    end
-endmodule
-</code>
-\\
-##### lfsr.v
-<code verilog>
-`timescale 1ns / 1ps
-module lfsr(
-    input clk,
-    input en,
-    input rst,
-    output [15:0]lfsr_out
-    );
-    //Create a 16-bit linear feedback shift register with
-    //maximal polynomial x^16 + x^14 + x^13 + x^11 + 1.
-    reg [15:0]lfsr = 16'd1;
-    wire feedback;
-    assign feedback = ((lfsr[15] ^ lfsr[13]) ^ lfsr[12]) ^ lfsr[10];
-    assign lfsr_out = lfsr;
-    //Update the linear feedback shift register.
-    always @(posedge clk) begin
-        if(rst) lfsr <= 16'd1;
-        else if(en) lfsr <= {lfsr[14:0], feedback};
-    end
-endmodule
-</code>
-\\
-##### TB_LMS_Adapt.v
-<code verilog>
-module TB_LMS_Adapt;
-    reg  clk = 1'b0;
-    reg  [7:0]sw = 1'b1;
-    wire [7:0]JA;
-    wire [15:0]d;
-    wire [15:0]y;
-    wire [15:0]e;
-    wire [15:0]n1;
-    filter_top uut(.clk(clk), .sw(sw), .JA(JA));
-    assign d = uut.fout;
-    assign y = uut.aout;
-    assign e = uut.err;
-    assign n1 = uut.af.n1[0];
-    always #5 clk = ~clk;
-    initial begin
-        //#20000000 sw[0] = 1'b1;
-        //#40000 sw[0] = 1'b1;
-    end
-endmodule
-</code>
-\\