Wavelets: Stop Letting Fourier Smear Your Transients
Building Practical, Good-Sounding Audio Effects in the Wavelet Domain
Real-time audio processing has a problem that hides in plain sight. It shows up when we want it the least, in the effects that we want the most. It starts with one tool we reach for all the time:
The Discrete Fourier Transform is fundamental in digital signal processing. But in order to get the most out of it, it needs a long window of signal; that's a luxury rarely given in real-time audio. With only a small chunk of the whole signal, the next logical choice is to use the Short-Time Fourier Transform. There's always a catch, though, and here it's a big one: when using the STFT, frequency resolution is tied to window length. The shorter the window (forced by a quicker transient), the coarser the frequency resolution becomes. This time-frequency trade-off, Heisenberg's principle but for signal processing, is baked into the maths of the STFT. This isn't ideal when some of the most important parts of audio, the snap of a snare, the pick of a guitar, are inherently short transients. So what can we do?
This is where the Wavelet Transform comes in. Instead of having to choose between frequency and time resolution, the Discrete Wavelet Transform allows for a mix of both, allocated to where they matter most: fine time resolution for sharp, high-frequency detail, and longer windows for the lower frequencies that underpin a sound. This multiresolution analysis is a technique that works naturally for audio and, surprisingly, is close to how human hearing works.
This talk introduces wavelets as a tool for developing good-sounding, practical audio effects. It will showcase before-and-after audio from a simple transient shaper, with just enough maths and computer science to tie it together (but not too much, don't worry). We'll also discuss the theory behind them and, just as importantly, when and why you'd reach for them over the traditional Fourier-based approach. And when you wouldn't.
D'Angelo Villarico Fitzpatrick
Test Engineer
Solid State Logic
D'Angelo graduated with a first-class MEng in Computer Science and Electronics from the University of Bristol in 2025, and now works as a test engineer at Solid State Logic, applying that academic grounding to professional audio gear.
D'Angelo got their start in audio technology when their Guitar Hero controller broke, and they tried to repair it. That led to repairing more gear, then to realising they could design and build it themselves. That interest slowly turned into a passion as breadboard circuits and Visual Basic tutorials became small-signal circuit analysis and DSP lectures. Now, as a fresh face in an experienced industry, they're keen to learn everything they can and pass it on as they go.