我正在制作一个带通滤波器，我根据正弦曲线创建了一些带有不需要的频率的信号：

Fs = 8e3; % Sampling Rate

fn = Fs/2; % Nyquist frequency

L = 1e3; % Length of signal

T = 1/Fs; % Sampling period

t = T*linspace(0,L,Fs); % Time domain

% Frequencies in Hz

f1 = 1500;

f2 = 700;

f3 = 2500;

f4 = 3500;

% Signal

x = 6*sin(2*pi*f1*t);

% Noise

noise = 3*sin(2*pi*f2*t)...

+ 2*sin(2*pi*f3*t)...

+ 1*sin(2*pi*f4*t);

x_noise = x + noise;

然后我创建一个Butterworth带通滤波器：

[b,a] = butter(10,[1000 2000]/fn,'bandpass');

带通响应(带freqz)的时间和频率空间信号如下所示：

我会从这里想出来，干脆做

xf = filter(b,a,x_noise);

我在这做错了什么？

这是完整的代码：

clear all

Fs = 8e3; % Sampling Rate

fn = Fs/2; % Nyquist frequency

L = 1e3; % Length of signal

T = 1/Fs; % Sampling period

t = T*linspace(0,L,Fs); % Time domain

% Frequencies in Hz

f1 = 1500;

f2 = 700;

f3 = 2500;

f4 = 3500;

% Signal

x = 6*sin(2*pi*f1*t);

% Noise

noise = 3*sin(2*pi*f2*t)...

+ 2*sin(2*pi*f3*t)...

+ 1*sin(2*pi*f4*t);

x_noise = x + noise;

subplot(221);

idx = 1:round(length(t)/30);

plot(t(idx),x(idx),t(idx),x_noise(idx));

xlabel('Time (s)'); ylabel('Signal Amplitudes');

legend('Original signal','Noisy signal');

% Frequency space

f = fn*linspace(0,1,L/2+1);

X = fft(x_noise)/L;

[b,a] = butter(10,[1000 2000]/fn,'bandpass');

h = abs(freqz(b,a,floor(L/2+1)));

subplot(222);

plot(f,abs(X(1:L/2+1)),f,h*max(abs(X)));

xlabel('Freq (Hz)'); ylabel('Frequency amplitudes');

legend('Fourier Transform of signal','Filter amplitude response');

% Filtered signal

xf = filter(b,a,x_noise);

subplot(223)

plot(t(idx),xf(idx));

xlabel('Time (s)'); ylabel('Signal Amplitudes');

legend('Filtered signal');

% Filtered in frequency space

Xf = abs(fft(xf)/L);

subplot(224);

plot(f,Xf(1:L/2+1),f,h*5e-6);

xlabel('Freq (Hz)'); ylabel('Frequency amplitudes');

legend('Fourier Transform of filtered signal','Bandpass');