A Practical Guide to Audio Distortion

When talking about "distortion," we often throw it into one of two buckets: an undesirable quality squashed as low as possible to impress fastidious audio engineers, or a revered sound transmutation that imparts mythical qualities to otherwise drab sounds. How can it be that these are the same animal?

This talk provides practical understanding for audio engineers, enthusiasts, and programmers of the two most fundamental types of audio distortion: harmonic and intermodulation. You'll learn what these distortions are and how they relate to basic math, dispel some common myths, better understand measurements, and gain conceptual tools to push your sound in new directions.

What this presentation is about and why it matters

This talk is a practical tour of audio distortion aimed at engineers, musicians, and DSP programmers who want to understand why certain nonlinear effects sound the way they do and how to control them. Instead of treating "distortion" as a single bad thing or a mystical flavor, the presenter separates the phenomena into three useful categories: harmonic distortion, intermodulation distortion, and aliasing (digital-only) distortion. Learning these distinctions matters because modern audio systems combine many nonlinear blocks (analog pedals, amp emulators, plugins), and the interaction between those blocks — not just a single harmonic measurement — determines perceived color, grit, fuzziness, or clarity.

Practically: if you design or use audio plugins, mix tracks that pass through multiple processors, or try to emulate analog gear, understanding which distortion products are being generated and how they fold back into the audible band (aliasing) will help you make better design and processing choices. The talk emphasizes sensible rules of thumb (e.g., prefer odd-order saturation for "cleaner" coloration, low-pass between nonlinear stages to avoid an "aliasing staircase") and explains why common unit tests (single-sine sweeps) can be misleading.

Who will benefit the most from this presentation

This is a beginner–intermediate talk aimed at people who already do some audio work but want clearer intuition:

• DSP engineers and plugin developers who implement nonlinear processing or emulations.
• Mixing and mastering engineers who want to diagnose why a chain of processors behaves unexpectedly.
• Instrument designers and pedal makers interested in the perceptual effects of saturation and overdrive.
• Students and hobbyists who know basic signals and want simple math-based intuition without heavy proofs.

What you need to know

The talk keeps the math light but expects familiarity with a few basic concepts. If you know these, you will get more out of the demos and explanations.

• Sine/cosine basics: a pure tone is a single-frequency sinusoid. Many identities below use cosines but sines are equivalent up to phase.
• Linear vs nonlinear systems: a linear system preserves addition and scalar multiplication; nonlinear systems do not and therefore create new frequencies.
• Fourier / spectrum intuition: multiplication in time corresponds to convolution in frequency; nonlinear time-domain operations spread and mix spectral content.
• Key trig identities used in the talk: these show how powers of a cosine generate harmonics. For example,
  $\cos^2 x = \tfrac{1}{2} + \tfrac{1}{2}\cos 2x$, which shows squaring produces a DC term and a second harmonic.
  $\cos^3 x = \tfrac{3}{4}\cos x + \tfrac{1}{4}\cos 3x$, which shows cubing keeps much of the original (fundamental) and adds a third harmonic.
• Chebyshev polynomials (brief mention): these polynomials relate $\cos(n x)$ to powers of $\cos x$ and explain how specific harmonics can be synthesized in the ideal single-tone case.
• Intermodulation: when two or more input frequencies are present, nonlinearities generate sums and differences (e.g., $A\pm B$, $2A\pm B$, ...), which are usually not musically aligned with the original pitches and often dominate the audible distortion.
• Nyquist and aliasing: in sampled systems any frequency above half the sample rate folds back (aliases) into the audible band, so generated high harmonics and intermodulation products can become audible artifacts.

Glossary

• Harmonic distortion — New frequency components at integer multiples of a single input tone (2×, 3×, etc.).
• Intermodulation distortion (IMD) — Products formed by sums and differences of two or more input frequencies (e.g., A+B, A−B, 2A±B).
• Saturation / Overdrive — Light-to-moderate nonlinear processing that "colors" sound by adding distortion products; often desirable.
• Aliasing — Digital folding of frequencies above Nyquist (fs/2) into the audible band, producing inharmonic artifacts.
• Nyquist frequency — Half the sampling rate; the highest representable frequency without aliasing in a sampled system.
• Chebyshev polynomials — Polynomial relationships that produce exact cosine multiples from powers of cosine for single-tone inputs.
• Even-order vs odd-order distortion — Even orders (squared, quartic) produce DC and stronger transient emphasis; odd orders (cubic, quintic) preserve more of the fundamental and sound "cleaner."
• Alias staircasing — The cumulative effect where nonlinear stages create high content that aliases, then further nonlinear processing re-modulates aliased content, producing more artifacts.
• Convolution (frequency domain) — The operation corresponding to time-domain multiplication; helps visualize how spectral components mix.
• DC offset — A non-zero constant term produced by even-order nonlinearities that may require filtering.

Final note — why watch this talk

This presentation strikes a rare balance between simple, usable math and audible, practical consequences. The speaker translates trig identities and polynomial expansions into clear listening takeaways (why cubic saturation often "sounds nicer," why sine-sweep tests can be misleading, and why low-pass filtering between nonlinear blocks helps). If you design, use, or tune audio processing chains, you will leave with actionable intuition and a checklist of things to try: listen for transient fuzziness, check for intermodulation products in real audio (not just single tones), and prevent needless aliasing with sensible oversampling and filtering. Its an approachable, honest talk that demystifies the colors of distortion without getting lost in theory — worth watching for anyone who wants to make or control pleasing distortion instead of accidentally creating noise.

This overview is AI-generated from the session transcript. Spot an issue? Let us know.