双二阶滤波器之MATLAB设计及C语言实现

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双二阶滤波器

本文中的例子和代码放在Github

First，什么是双二阶滤波器？wiki上是这么说的：二阶、递归、线性，含有两个极点和两个零点，“双二阶”的名字来源于它的传递函数是两个二次多项式的比值。

In signal processing, a digital biquad filter is a second order recursive linear filter, containing two poles and two zeros. “Biquad” is an abbreviation of “biquadratic”, which refers to the fact that in the Z domain, its transfer function is the ratio of two quadratic functions: H(z)=(b₀+b₁z⁻¹+b₂z⁻²)/(a₀+a₁z⁻¹+a₂z⁻²) The coefficients are often normalized such that a₀ = 1: H(z)=(b₀+b₁z⁻¹+b₂z⁻²)/(1+a₁z⁻¹+a₂z⁻²) High-order IIR filters can be highly sensitive to quantization of their coefficients, and can easily become unstable.

归一化传递函数写成这样：
$$H(z)=\frac{b₀+b₁z⁻¹+b₂z⁻²}{1+a₁z⁻¹+a₂z⁻²}$$

用MATLAB的Filter Designer来设计一个：400Hz带通IIR，需要用4个Sections来实现，默认给出的滤波器结构是Direct-Form II。

在菜单栏的Analysis中选择Filter Coeffients就能看到滤波器系数了：

Numerator，分子，也就是传递函数中的b项们，从上到下依次为$b_0$，$b$

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