Skill v1.0.0
currentAutomated scan100/100version: "1.0.0" name: dsp-algorithm-guide description: > Implementation guide for common DSP algorithms. Use when the user asks "implement a lowpass filter", "how do I write a compressor", "reverb algorithm", "FFT convolution", "pitch shifter", or "oscillator with no aliasing". Trigger on phrases like "biquad filter", "state variable filter", "feedback delay network", "phase vocoder", "overlap-add", "PolyBLEP", or any request to implement a specific DSP processing block.
DSP Algorithm Guide
Three steps: pick the right algorithm family, address implementation concerns, then verify correctness.
Step 1 — Identify the algorithm family
| User request | Algorithm family | Recommended starting point | |
|---|---|---|---|
| Lowpass / highpass / bandpass / notch | Biquad (IIR) | Direct Form II transposed | |
| High-quality parametric EQ, resonant filter | Biquad cascade or SVF | State Variable Filter (SVF) | |
| Shelving / high-shelf / low-shelf | Biquad (Audio EQ Cookbook) | Peaking EQ or shelf coefficients | |
| Reverb (algorithmic) | FDN or Schroeder/Moorer | Feedback Delay Network (FDN) | |
| Reverb (convolution / IR) | OLA / OLS | Overlap-Add with FFT | |
| Compressor / limiter / expander / gate | Level detector + gain computer | RMS or peak detector + knee curve | |
| Pitch shift / time stretch | Phase vocoder or granular | Phase vocoder for tonal material | |
| Anti-aliased oscillator | BLIT / PolyBLEP / wavetable | PolyBLEP for simple waveforms | |
| Spectral processing / analysis | STFT pipeline | Overlap-Add / Overlap-Save | |
| Waveshaper / saturation | Memoryless nonlinearity | Soft-clip with oversampling |
Step 2 — Implementation concerns
Work through this checklist before writing any DSP code:
- [ ] Stability — confirm the algorithm's stability condition and check it after every coefficient update (e.g., biquad poles inside unit circle).
- [ ] Coefficient precision — use
doublefor coefficient computation; cast tofloatfor the inner loop only if profiling demands it. - [ ] Denormal protection — use
ScopedNoDenormals/FTZ where available, or add explicit state clamps/noise around feedback paths. - [ ] Latency reporting — if the algorithm introduces latency (e.g., FFT block size), call
setLatencySamples()so the host can compensate. - [ ] Initialisation — clear all delay-line and state memory in
prepareToPlay; never assume zero-init across transport loops. - [ ] Parameter smoothing — ramp filter coefficients or gain values over a block; abrupt changes cause clicks and, for IIR filters, instability.
- [ ] Oversampling — nonlinear stages (waveshapers, saturators) need at least 2x oversampling to suppress alias products.
Step 3 — Test the implementation
- [ ] Frequency response: compare magnitude/phase against the reference formula at multiple frequencies (e.g., plot with Python or MATLAB).
- [ ] Step response: feed a unit step; verify overshoot and decay match the algorithm's expected behaviour.
- [ ] Silence-in → silence-out: verify the output reaches and stays at zero after silent input (no denormal crawl).
- [ ] No NaN / Inf: run with extreme parameter values (fc = 1 Hz, fc = Nyquist − 1 Hz, gain = 0 dB, gain = +24 dB).
- [ ] Impulse response (convolution / reverb): verify IR matches the target via inverse FFT.
- [ ] CPU profiling: measure per-block worst case before shipping; compare against the buffer deadline on the target CPU instead of relying on fixed ns/sample budgets.
See references/algorithm-cookbook.md for difference equations, stability conditions, coefficient mappings, and numerical tips for each family.