Pulling a sound apart — separation, modeling, and gap-filling

The tools so far mostly subtract a problem — hum, hiss, a click. This chapter is about three deeper moves: splitting a sound into layers, rebuilding it from a model, and filling in pieces that are missing entirely.

Harmonic vs. percussive — the HPSS split

Look at a spectrogram (the time × frequency picture from the “two views” chapter). Two kinds of things live there, and they look completely different:

• Tonal sounds — a held note, a hum, a vowel — draw horizontal lines. They sit at one pitch and last a while.
• Percussive sounds — a drum hit, a click, a consonant — draw vertical lines. They’re brief but splash across every frequency at once.

That visual difference is a handle you can grab. Run a filter along time and you keep the horizontal streaks (the tonal part). Run one along frequency and you keep the vertical streaks (the percussive part). That’s HPSS — harmonic / percussive source separation — and it needs no AI, just two median filters:

cathar hpss song.wav --harmonic tonal.wav --percussive hits.wav

The two outputs add back up to the original exactly. It’s a fast way to pull the drums out from under a melody, or to treat the “attack” of a recording separately from its “sustain”.

Rebuilding from a model — sinusoidal synthesis

Here’s a stronger idea: instead of filtering a sound, describe it and build a fresh one from the description.

Most musical, voiced sound is a stack of steady tones — partials. cathar sms (sinusoidal modeling synthesis) finds the peaks in each moment’s spectrum, tracks each one as it glides through time, and then re-synthesises the whole recording from those tracked partials alone:

cathar sms noisy-flute.wav        # keep the tones, drop everything else

Because hiss, breath, and crackle don’t form steady tracked partials, they simply aren’t rebuilt — they fall away. The result is a “tonal purify”: the musical skeleton of the sound, with the stochastic fuzz left behind. Push it and it sounds synthetic (it is synthetic — you rebuilt it); used gently it’s a striking way to isolate the pure tone from a noisy capture.

Filling holes — audio inpainting

Sometimes samples aren’t just damaged, they’re gone: a drop-out on a bad transfer, a splice in a tape, a mute where a CD skipped. There’s nothing to subtract — you have to invent the missing stretch so it can’t be heard.

The trick is the same one your ear uses to finish a sentence someone mumbled: predict from context. Cathar fits a short mathematical model to the audio on both sides of the hole — one that captures the local pitch and shape — and then solves for the samples that continue smoothly in from the left and out to the right at the same time:

cathar inpaint dropout.wav --start-ms 1240 --len-ms 8   # patch a known gap
cathar inpaint transfer.wav                              # auto-find & fill mutes

This is the classic Janssen / autoregressive method, and it’s genuinely good for short gaps — up to a few milliseconds. Ask it to invent a whole word and it can’t; the model only knows what the surrounding audio implies.

The dense cousin — de-crackle

Vinyl has a special kind of damage: not the occasional loud pop (that’s a job for declick) but a constant field of tiny crackles, thousands of them, like frying bacon under the music. cathar decrackle hunts for those little spikes — each one a sample or two that jumps away from its neighbours — and smooths each back into place, without touching the music around it:

cathar decrackle old-lp.wav --sensitivity 5

Between declick for the big pops, decrackle for the fine sizzle, and inpaint for the outright holes, the whole spectrum of “missing or broken samples” is covered.