如何在matlab中不使用内置函数构建低通滤波器

Question

我有一个复杂的频率信号（我已从时域转换）。现在我想在切断频率值的同时实现低通滤波器。有人可以建议我在不使用内置函数（过滤器）的情况下实现低通滤波器的最佳方法。

Answer 1

我建议你看看Robert Bristow-Johnson的Audio-EQ-Cookbook，你可以建立很多过滤器。

让我们尝试按照公式建立一个LPF（低通滤波器），首先我建立一个信号测试（四个正弦波在200,500,700和1000Hz），FFT图：

现在应用方程式来切断200hz的频率

我的代码用于测试：

%Low pass filter example from RBJ EQ-Cookbook
N = 4096;

%Test signal

Fs=44100;
f1  = 200;
f2  = 500;
f3  = 700;
f4  = 1000;

signal1 = 0.9*sin(2*pi*f1/Fs*(0:N+1));

signal2 = 0.9*sin(2*pi*f2/Fs*(0:N+1));

signal3 = 0.9*sin(2*pi*f3/Fs*(0:N+1));

signal4 = 0.9*sin(2*pi*f4/Fs*(0:N+1));


%mix all signals
signal= signal1 + signal2 + signal3  + signal4;

%test signal end

%%Start Filter

%F0 - cut off Frequency above ??
F0 = 200;
Q=1;
g = 80;

A = sqrt (10^(g/20));
w0 = 2 * pi * F0/Fs;
c= cos(w0);
s = sin(w0);

alpha = sin(w0)/(2*Q);


b0 = (1 - cos(w0))/2;
b1 = 1 - cos(w0);
b2 = (1- cos(w0))/2;
a0 = 1 + alpha;
a1 = -2*cos(w0);
a2 = 1 - alpha;

x1 = 0;
x2 = 0;
y1 = 0;
y2 = 0;

b0 = b0 / a0;

b1 = b1 / a0;

b2 = b2 / a0;

a1 = a1 / a0;

a2 = a2 / a0;


%y = filtred signal
for j=1:length(signal),

    y(j) = b0*signal(j) + b1*x1 + b2*x2 - a1*y1 - a2*y2;

    x2 = x1;
    x1 = signal(j);
    y2 = y1;
    y1 = y(j);

end