Bilinear Transform For IIR Filter Design Explained Intuitively [AudioFX #007]

✅ Check out the full article on TheWolfSound.com: https://www.thewolfsound.com/bilinear... ✅ Sign up for WolfSound's newsletter: https://thewolfsound.com/newsletter/ ✅ Please subscribe to WolfSound to let the little Wolf 🐺 grow: https://www.youtube.com/c/WolfSoundAu... 🎧 Listen to my music: https://thewolfofficial.com/ Hi, my name is Jan Wilczek and I am an audio programmer and a researcher. Welcome to WolfSound! WolfSound's mission is to provide high-quality, informative, and entertaining videos, articles, and courses on how to process sound by exploring mathematics, applying algorithms, and creating code in various programming languages. Topics include sound synthesis, digital signal processing, programming languages for audio (C, C++, Python, Rust), and audio effects. I am also sharing tips on how to learn fast and effectively. Make sure to visit https://www.thewolfsound.com/. WolfSound enables everybody to learn about audio programming! 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. ABOUT ME 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 Programming (...   FOLLOW WOLFSOUND ONLINE ✅ Blog: https://www.thewolfsound.com/ ✅ LinkedIn:   / jan-wilczek-audio-programmer   ✅ Twitter:   / wilczek_jan   ✅ Facebook:   / janwilczekwolfsound   ✅ Instagram:   / janwolfwilczek   ✅ Pinterest:   / jawitrle   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