Where to learn about "analog prototype filters"?

Where to learn about "analog prototype filters"?

I've heard about them, but I'm unsure about what they really are and how they're constructed.

• Do you want op-amp circuits? The Audio EQ Cookbook will give your $H(s)$ transfer functions for standard second-order analog filters. But if you want circuits, start with the Sallen-Key. Google that. Also there is an EE stack exchange. Commented Jan 17, 2022 at 22:42

"Analog prototype" filters are well-known analog filters that have specific desirable properties. They include (but aren't limited to):

These prototypes can be used to design digital filters that have approximately the same characteristics, for instance by using the bilinear transform.

• Why are they called analog? Commented Aug 16, 2018 at 15:53
• Because they are physical objects that operate on analog signals. Commented Aug 16, 2018 at 15:55
• Note that for the Bessel filter, the bilinear transform will not result in a discrete-time filter that is optimal in any sense, because the frequency warping will affect the maximally flat group delay property. All other analog filters mentioned in this answer will retain their optimality when transformed by the bilinear transform. Commented Aug 16, 2018 at 16:34
• @mavavilj they are “analog” in the sense that one can implement the filter in the continuous time domain (via design using Laplace transforms) using analog electronic components (resistors, inductors, capacitors), rather than discrete digital filters using the Z-transform. See Matt L.’s response regarding the bilinear transform as it’s a very important thing to note. Commented Aug 17, 2018 at 2:03
• Also resist the temptation to design a digital filter by copying an analog prototype (unless there is specific reason to do so, such as modelling an analog system). In most cases direct digital filter design algorithms will result in the best filter implementation. Analog is limited by the realizable components (inductors, capacitors etc) while digital is limited by the math and precision available. This holds true for many aspects of signal processing design where a relationship to a known analog process can be instructive, but be cautious in simply copying an analog implementation. Commented Aug 18, 2018 at 1:47

In the domain of digital audio effects, analog filters (called analog prototype filters or analog prototypes) are used to derive stable and controllable digital infinite-impulse response (IIR) filters.

These filters can then be used by musicians or sound engineers, for example, in parametric equalizers.

If you are interested in the topic, I have a few materials that extend the topic:

1. What is an analog prototype filter and how to design it article video
2. How to digitize the analog prototype with the bilinear transform article