如何使用Matlab做一个简单的FIR滤波器？ [英] How to make a Simple FIR Filter using Matlab?

问题描述

如何使用Matlab（不使用内置函数）做一个简单的低通FIR滤波器？

问题示例：

 执行截止频率为250Hz的FIR LPF 
  

可能还需要取样频率给定...

解决方案尝试或者我已经知道的：

  x = [...]  - >输入信号
 A = 1; - >由于这是FIR 
 B = [
 y] = filter（B，A，x） - >输出信号
  

Afaik，B应包含FIR滤波器的系数。但;我怎么计算这些系数给定我只有截止频率？最简单的事情是一个窗口sinc filter：

  fs = 44100; 
 cutoff = 250; 
 t = -256：256; ％这将是一个513抽头滤波器
 r = 2 * cutoff / fs; 
 B = sinc（r * t）* r。* blackman（length（t））'; 
 freqz（B）; 
  

过滤器的长度（参见 t = ... ）控制过渡带的宽度。在这种情况下， cutoff 是-6 dB点。 blackman 是一个受欢迎的窗口的名称。您可以查看这个维基百科页面以获取更多关于窗口功能的信息。它们在转换带宽和阻带抑制之间基本上有不同的权衡。

How can I make a simple low-pass FIR filter using Matlab (without using the built-in function) ?

Problem example:

Implement a FIR LPF with cut-off frequency 250Hz

it may also be necessary that, sampling freq is given...

Solution attempt or what I already know:

x = [...] -> input signal
A = 1; -> Since this is FIR
B = [?????]
y = filter(B, A, x) -> Output signal

Afaik, B should contain the coefficients for the FIR filter. But; how do I calculate these coefficients given that I only have the cut-off frequency?

解决方案

The simplest thing is a "windowed sinc" filter:

fs = 44100;
cutoff = 250;
t = -256:256;  % This will be a 513-tap filter
r = 2*cutoff/fs;
B = sinc(r*t).*r .* blackman(length(t))';
freqz(B);

The length of the filter (see t=...) controls the width of the transition band. cutoff is in this case the -6 dB point. blackman is the name of a popular window. You can check out this Wikipedia page for more infos on window functions. They basically have different trade-offs between transition band width and stopband rejection.

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