5.4. Transforming Analog Filters into Digital Filters

In this chapter we focus on analog filters as defined in the s-domain and introduce the bilinear transform to make such an analog filter into a digital filter.

First we discuss the analog prototype filters (Low-pass, High-pass etc) and discuss the transfer functions of these filters as expressed in the s-domain.

Then we discuss the bilinear transform as a way to transform an analog filter into a digital filter.

Finally we give some examples of discrete IIR filters that are defined through the bilinear transform. We will discuss and show how these filters can be run in realtime in Python code.

• 5.4.1. Analog Filters
  • 5.4.1.1. Ideal Filters
  • 5.4.1.2. The Canonical (Low Pass) First Order Filter and its Transformations
    • 5.4.1.2.1. Selecting the Corner Frequency
    • 5.4.1.2.2. From Low Pass to High Pass
    • 5.4.1.2.3. From Low Pass to Bandpass
  • 5.4.1.3. Second Order Filters
    • 5.4.1.3.1. From Low Pass to High Pass
    • 5.4.1.3.2. Second Order Filters from the (Audio) Cookbook
  • 5.4.1.4. Higher Order Filters
• 5.4.2. From Analog to Digital through the Bilinear Transform
  • 5.4.2.1. The Bilinear Transform
  • 5.4.2.2. Pre-Warping
• 5.4.3. IIR Filters in Python
• 5.4.4. Exercises