Bilinear Transform For IIR Filter Design Explained Intuitively [AudioFX

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Hi, my name is Jan Wilczek and I am an audio programmer and a researcher. Welcome to WolfSound!

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ABOUT THE VIDEO

In this video, you will learn how to digitize analog music systems with the bilinear transform. The bilinear transform is a change of variables, mapping the jω frequency axis of the s-plane to the unit circle of the z-plane. It converts stable analog systems into stable digital systems so it is useful for the design of IIR digital filters from analog filters. However, it distorts the frequencies (frequency warping) what can be counteracted with prewarping. The video contains the derivation and properties of the bilinear transform. It also shows you an example of a bilinear transform of the second-order analog Butterworth lowpass, which results in an IIR filter.

In case of any doubt in understanding, please, refer to the article above or ask a question in the comments 🙂

Video edited by Jorge Jimenez and Jan Wilczek.

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My name is Jan Wilczek. I am an audio programmer, a researcher in the field of music technology, and a musician. Through articles and videos from WolfSound, you will easily understand the main concepts of sound processing using software. My full story:    • How I Got Started With Audio Programm...  

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TIME CODES

00:00 Introduction
00:37 Recap
01:05 Digitization goal
01:25 Bilinear transform definition
02:20 Bilinear transform derivation
09:43 Properties of the bilinear transform
11:38 Frequency warping
12:29 Prewarping
13:49 Example: second-order Butterworth lowpass digitization.
15:01 Summary

#dsp #filters