An Introduction to Digital Filters

🎯 Learning Objectives

• Describe the typical stages in an audio processing pipeline.
• Explain the role of each stage from acquisition to reproduction.

📚 Overview

Digital signal processing, and for us audio files and for the musicians, the audio signal processing is a fascinating area of study. In it, encompasses all of the audio effects that we know and love including:

• Filters
• Delays
• Reverbs
• Modulators
• Dynamic processors such as compressors and limiters
• Non-linear processors like distortion saturation
• Phase work orders
• Pitch shifters

Many books and resources on these topics failed to mention is that the mathematics is complex. Not necessarily complicated, but a fundamental understanding of complex numbers, complex algebra is required to understand a wide variety of textbooks related to the discussion of DSP. And once you get into them you quickly realize that it doesn't just end there you need to understand:

• Complex sinusoids
• Z-transforms and
• Fourier transforms

which convert discrete and continuous time complex signals to their frequency domain representation on a healthy understanding of trigonometry Vector geometry and calculus. And that's when we choose to close the book and fend off an eternal sense of dread and insecurity. For a lot of people getting into DSP has a high barrier for entry.

Intuitively understanding these subjects irrespective of the math is a sure fire way of building foundational understanding and interest in the subject. So this entire topic is dedicated to the discussion of one of the core areas of DSP and an effect that's widely used in every realm of audio processing, i.e. “filters”. We will approach filtering with as little complex mathematics as possible and rather rely on an analytical approach of simulation and visualizations to get an intimate understanding of filters;

How they work and how they behave

🧪 Python Example

Press Run Code: Output will appear here.

🧠 Quick Quiz

📚 References

• B. Pohlmann, Principles of Digital Audio.
• Wikipedia: Digital signal processing