MATLAB实现FIR滤波器仿真与优化

 x=0.0003125:0.0003125:0.05; %采样频率设为3.2KHz即每个周期含有64个采样点
 s=220*sqrt(2)*sin(2*pi*50*x); %电网原信号
 n0=rand(1,160)*11; %白噪声
 n5=11*sqrt(2)*sin(2*pi*250*x+2*rand(1,1)*pi); %5次谐波
 n7=11*sqrt(2)*sin(2*pi*350*x+2*rand(1,1)*pi); %7次谐波
 n11=11*sqrt(2)*sin(2*pi*550*x+2*rand(1,1)*pi); %11次谐波
 n13=11*sqrt(2)*sin(2*pi*650*x+2*rand(1,1)*pi); %13次谐波
 n17=11*sqrt(2)*sin(2*pi*850*x+2*rand(1,1)*pi); %17次谐波
 y=n0+n5+n7+n11+n13+n17+s; %采样到的电网信号
 figure(1);subplot(2,1,1);plot(x,s);grid on;title('原电压信号');
 figure(1);subplot(2,1,2);plot(x,y,'r');grid on;title('以3.2KHz采样频率采样到的电网电压信号');
 Vs= sqrt(sum(s.^2)/length(s));%得到有效值
 Vy= sqrt(sum(y.^2)/length(y));%得到有效值
 Ve=abs(Vy-Vs)/Vs;%计算测量电压有效值的相对误差
 Ps=max(s)-min(s);%计算原电压信号峰值Ps=max(s)-min(s);%计算原电压信号峰值
 Py=max(y)-min(y);%计算采样到的电压信号峰值
 Pe=abs(Ps-Py)/Ps;%计算测量电压峰值的相对误差
 Fpass = 55;    % 通带频率
 Fstop = 245;   % 阻带频率
 Fs    = 3200;  % 采样频率
 Wp = Fpass*2*pi/Fs; Ws = Fstop*2*pi/Fs;  deltaw= Ws - Wp;        % 过渡带宽Δω的计算
 Normal_N = ceil(6.6*pi/ deltaw) + 1;    % 按海明窗计算所需的滤波器阶数N
 N_wdham = (hamming(Normal_N+1))';        % 海明窗计算
 Wn=(Fpass+Fstop)/Fs;                   % 计算截止频率
 Normal_hamming=fir1(Normal_N,Wn,N_wdham);
 New_N=64;%滤波器阶数设为与一周期内采样点数相同的阶数
 New_wdham = (hamming(New_N+1))';        % 海明窗计算
 New_hamming=fir1(New_N,Wn,New_wdham);
 af_Normal=filter(Normal_hamming,1,y);
 af_New=filter(New_hamming,1,y);