Conversion of analog filter to digital filter

In the previous blog "The Principle and implementation of IIR Gaussian filtering", we have mentioned the transformation from the S domain to the z domain, that is, the analog filter into the digital filter

Wave Device, This article will formally introduce this issue. for IIR filter design, there are two common methods: Impulse invariance and bilinear transformation, this paper will focus on

elaborated two kinds of the principle of the method. Set the analog filter system function to H (s), the digital filter system function is H (z), we need to do is to create S to Z

, from H (s) to derive H (z).

Impulse does not change the first of H (s) to the Laplace inverse transformation of the Unit Impulse response H (t), H (t) sampling to get h[n], and then to H[n] Z-transformation

to H (z). Because the impulse response of the digital filter is the sampling of the impulse response of the analog filter, the time-domain approximation characteristic of the filter is good. Assumptions

H (s) is a rational polynomial, and only the unfiltered pole, the use of fractional fraction is expressed as follows:

Conversion of analog filter to digital filter