Matlab

butter函数：巴特沃斯模拟和数字滤波器设计详细解释如下：

butter Butterworth digital and analog filter design.

[B,A] = butter(N,Wn) designs an Nth order lowpass digital Butterworth filter and returns the filter coefficients in length

N+1 vectors B (numerator) and A (denominator). The coefficients are listed in descending powers of z. The cutoff frequency Wn must be 0.0 < Wn < 1.0, with 1.0 corresponding to half the sample rate.

If Wn is a two-element vector, Wn = [W1 W2], butter returns an order 2N bandpass filter with passband W1 < W < W2. [B,A] = butter(N,Wn,'high') designs a highpass filter. [B,A] = butter(N,Wn,'low') designs a lowpass filter.

[B,A] = butter(N,Wn,'stop') is a bandstop filter if Wn = [W1 W2]. When used with three left-hand arguments, as in

[Z,P,K] = butter(...), the zeros and poles are returned in length N column vectors Z and P, and the gain in scalar K. When used with four left-hand arguments, as in

[A,B,C,D] = butter(...), state-space matrices are returned. butter(N,Wn,'s'), butter(N,Wn,'high','s') and butter(N,Wn,'stop','s') design analog Butterworth filters. In this case, Wn is in [rad/s] and it can be greater than 1.0

需要注意的是，Wn不能⼤于1，Wn = 1相当于fs/2。例1：

t = 0:0.001:1;

x = sin(t*2*pi*200)+ sin(t*2*pi);[b,a] = butter(10,0.2);figure(1);freqz(b,a);y = filter(b,a,x);figure(2)

subplot(2,1,1);plot(x);subplot(2,1,2);plot(y);结果：

例2：⽣成⼀个采样频率为2000，由50Hz、120Hz、200Hz、正弦信号及噪声信号组成的数字信号，滤掉⼩于150Hz的频率，计算并显⽰滤波前后的原始数据波形以及功率谱密度

下⾯是代码，其中[Y,f] = Spectrum_Calc(y,Fs);函数的具体代码见http://blog.sina.com.cn/s/blog_84024a4a01015rez.htmlclose allclear allclc

Fs=2000;Fa=Fs/2;N=512;t=0:1/Fs:1;

x=2*sin(t*2*pi*50)+sin(t*2*pi*120)+3*sin(t*2*pi*200)+randn(1,length(t));

% [b,a]=butter(10,[100/Fa 150/Fa],'stop');[b,a]=butter(10,150/Fa,'high');figure(1);freqz(b,a);y=filter(b,a,x);figure(2);

subplot(2,1,1);plot(x);subplot(2,1,2);plot(y);figure(3);

subplot(2,1,1);

[Y,f] = Spectrum_Calc(x,Fs);P=Y.*conj(Y)/N; plot(f,Y);

figure(3);

subplot(2,1,2);

[Y,f] = Spectrum_Calc(y,Fs);P=Y.*conj(Y)/N; plot(f,Y);运⾏结果：fourier变换的幅频图

功率谱密度图，这⾥需要将上⾯的plot(f,Y);换为plot(f,P);从功率谱和幅频图上看，效果是很好的。

另外我还尝试了带阻滤波器，但是效果不好，⽆法得到预期图像。