作者：OpenSLee

在《基于FPGA的多級CIC濾波器實現(xiàn)四倍抽取一》和《基于FPGA的多級CIC濾波器實現(xiàn)四倍抽取二》中我們先來了解滑動平均濾波器、微分器、積分器以及梳狀濾波器原理以及它們的幅頻響應(yīng)。此篇我們將用verilog實現(xiàn)基于FPGA的多級CIC濾波器實現(xiàn)四倍插值。

1 CIC濾波器的基本概述

CIC（積分梳狀）濾波器是無線通信中的常用模塊，一般用于數(shù)字下變頻（DDC）和數(shù)字上變頻（DUC）系統(tǒng)。CIC濾波器結(jié)構(gòu)簡單，只有加法器、積分器和寄存器，適合于工作在搞采樣率條件下，而且CIC濾波器是一種基于零點相消的FIR濾波器，已經(jīng)被證明是在高速抽取或插值系統(tǒng)中非常有效的單元。

整數(shù)倍內(nèi)插是先在已知抽樣序列的相鄰兩個抽樣點之間等間隔地插入（I-1）個零值點，然后進行低通濾波器，即可求得I倍內(nèi)插的結(jié)果。

此篇我們采用多級CIC濾波器實現(xiàn)整數(shù)倍內(nèi)插提升采樣率。

2 matlab實現(xiàn)CIC濾波器的四倍插值

設(shè)計目標(biāo)：將載波頻率44.1khz的1khz sine升采樣率到176.4khz。

close all
clear all
clc

%set system parameter
fs = 1000;    %The frequency of the local oscillator signal
Fs = 44100;   %sampling frequency
Fs1 = 176400;
N =  24;         %Quantitative bits
L = 81920;

%Generating an input signal
t =0:1/Fs:(1/Fs)*(L-1);          %Generating the time series of sampling frequencies
sc =sin(2*pi*fs*t);        %a sinusoidal input signal that produces a random starting phase

b =[1,-1];%comb
a =[1,-1];%integerator

%comb
c1=filter(b,1,sc);
c2=filter(b,1,c1);
c3=filter(b,1,c2);

y = upsample(c3,4);

%integerater
i1 =filter(1,a,y);
i2 =filter(1,a,i1);
i3 =filter(1,a,i2);
sf = i3./16;

f_osc =fft(sc,L);
f_osc=20*log(abs(f_osc))/log(10);        %換算成dBW單位
ft1=[0:(Fs/L):Fs/2];              %轉(zhuǎn)換橫坐標(biāo)以Hz為單位
f_osc=f_osc(1:length(ft1));

f_o =fft(sf,L);
f_o=20*log(abs(f_o))/log(10);        %換算成dBW單位
ft2=[0:(Fs1/L):Fs1/8];              %轉(zhuǎn)換橫坐標(biāo)以Hz為單位
f_o=f_o(1:length(ft2));

figure(1),
subplot(211),stem(t(1:32),sc(1:32));
xlabel('時間(t)','fontsize',8);
ylabel('幅度(dB)','fontsize',8);
title('sc','fontsize',8);
subplot(212),stem(t(1:128),sf(1:128));
xlabel('時間(t)','fontsize',8);
ylabel('幅度(dB)','fontsize',8);
title('sf','fontsize',8);

figure(2),
subplot(211),plot(ft1,f_osc);
xlabel('頻率(Hz)','fontsize',8); ylabel('功率(dBW)','fontsize',8);
title('原始信號信號頻譜圖','fontsize',8);legend('sc');
subplot(212),plot(ft2,f_o);
xlabel('頻率(Hz)','fontsize',8); ylabel('功率(dBW)','fontsize',8);
title('濾波后信號頻譜圖','fontsize',8);legend('sf');

3 FPGA實現(xiàn)CIC濾波器的四倍插值

FPGA設(shè)計：FPGA由i2s輸入44.1khz的1khz sine（當(dāng)然也可以是歌曲44.1khz采樣率），經(jīng)過i2s串轉(zhuǎn)并后經(jīng)過mult_cic模塊進行采樣率提升處理（變成176.4khz 1khz sine或者歌曲），再通過i2s_tx_master并轉(zhuǎn)串送到DAC 。

多級CIC濾波器的結(jié)構(gòu)主要由梳狀濾波器+插值+積分器構(gòu)成。

FPGA代碼：

`timescale 1ps/1ps
 
module mult_cic#(parameter DW = 38)(
       input mclk,//45.1584MHZ
   input reset_n,
   input signed[31:0] pcm_in,//44.1khz
   output signed[31:0] pcm_out //176.4khz
   );
 
wire signed [DW-1:0]       temp;
wire signed [DW-1:0]integrator_temp;
wire signed [DW-1:0]    interpolation_temp;
wire signed [DW-1:0]    comb_temp;  
 
assign temp = {{(DW-32){pcm_in[31]}},pcm_in};
 
comb#(.DW(DW))
      U_comb(
     .mclk(mclk),
 .reset_n(reset_n),
 .din(temp),
 .dout(comb_temp)
 );   
interpolation#(.DW(DW))
        U_interpolation(
       .mclk(mclk),
   .reset_n(reset_n),
   .din(comb_temp),
   .dout(interpolation_temp)
   );
   
 
integrator#(.DW(DW))
        U_integrator(
           .mclk(mclk),
       .reset_n(reset_n),
       .din(interpolation_temp),
       .dout(integrator_temp)
   );
   
 
//divide
assign pcm_out = integrator_temp[35:4];   
endmodule

module integrator#(parameter DW = 38)(
       input                mclk,
   input                reset_n,
   input  signed [DW-1:0] din,
   output signed [DW-1:0] dout
   );
 
localparam LAST_CYCLE = 256;
reg [7:0] i;
 
reg signed [DW-1:0] temp_xin1,temp_xin2,temp_xin3;
wire signed [DW-1:0] i1_temp,i2_temp,i3_temp;
 
always @(posedge mclk or negedge reset_n) begin
  if(reset_n == 1'b0)
    i <= 0;
  else
    i < = i+1;
end
 
always @(posedge mclk or negedge reset_n) begin //The first level integrator
  if(reset_n == 1'b0)
    temp_xin1 <= 0;
  else if(i == (LAST_CYCLE-1))
    temp_xin1 <= i1_temp;
end
 
assign i1_temp = (reset_n == 1'b0)?38'b0:( din + temp_xin1);
 
always @(posedge mclk or negedge reset_n) begin //The second level integrator
  if(reset_n == 1'b0)
    temp_xin2 <= 0;
  else if(i == (LAST_CYCLE-1))
    temp_xin2 <= i2_temp;
end
 
assign i2_temp = (reset_n == 1'b0)?38'b0:( i1_temp + temp_xin2);
 
always @(posedge mclk or negedge reset_n) begin //The third level integrator
  if(reset_n == 1'b0)
    temp_xin3 <= 0;
  else if(i == (LAST_CYCLE-1))
    temp_xin3 <= i3_temp;
end
 
assign i3_temp = (reset_n == 1'b0)?38'b0:( i2_temp + temp_xin3);
 
assign dout = i3_temp;   
 
endmodule

module interpolation#(parameter DW = 38)(
       input                mclk,
   input                reset_n,
   input  signed [DW-1:0] din,
   output signed [DW-1:0] dout
   );
   
localparam LAST_CYCLE = 256;
reg [9:0] i;
 
reg signed [DW-1:0] dout_pcm;
 
assign dout = dout_pcm;
 
always @(posedge mclk or negedge reset_n) begin
  if(reset_n == 1'b0) begin
    i <= 0;
dout_pcm<=0;
  end
  else begin
    i <= i+1;
if(i == (LAST_CYCLE-1)) dout_pcm<=din;      //upsample(x,n)--n--4
if(i == (LAST_CYCLE*2-1)) dout_pcm<=32'b0;      //upsample(x,n)--n--4
if(i == (LAST_CYCLE*3-1)) dout_pcm<=32'b0;      //upsample(x,n)--n--4
if(i == (LAST_CYCLE*4-1)) dout_pcm<=32'b0;      //upsample(x,n)--n--4
  end
end
 
endmodule

module comb#(parameter DW = 38)(
       input                mclk,
   input                reset_n,
   input  signed [DW-1:0] din,
   output signed [DW-1:0] dout
   );
   
localparam LAST_CYCLE = 1024;
reg [9:0] i;//88.2
 
reg signed [DW-1:0] d1,d2,d3,d4;
wire signed [DW-1:0] c1,c2;
 
always @(posedge mclk or negedge reset_n) begin
  if(reset_n == 1'b0) begin
    i <= 0;
d1 <=0;
d2 <=0;
d3 <=0;
d4 <=0;
  end
  else begin
    i <= i+1;
if(i == (LAST_CYCLE-1)) begin
      d1<=din;
  d2<=d1;
  d3<=c1;
  d4<=c2;
end
  end
end
 
assign c1 = (reset_n ==1'b0)?38'b0:(d1-d2);//comb1
assign c2 = (reset_n ==1'b0)?38'b0:(c1-d3);//comb2
assign dout =(reset_n ==1'b0)?38'b0:(c2-d4);//comb3
 
endmodule

FPGA仿真：

仿真輸入1khz sine輸出依然為1khz sine，設(shè)計成功。

至此我們可以去完成3倍抽取5倍插值等采樣率轉(zhuǎn)化算法。

編輯：hfy