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dsp-algorithm-guide

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.

kunitoki/sonic-skills
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  • SKILL.md3.6 KB
  • references/algorithm-cookbook.md6.9 KB

SKILL.md（原文）

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DSP Algorithm Guide

Three steps: pick the right algorithm family, address implementation concerns, then verify correctness.

Step 1 — Identify the algorithm family

User requestAlgorithm familyRecommended starting point
Lowpass / highpass / bandpass / notchBiquad (IIR)Direct Form II transposed
High-quality parametric EQ, resonant filterBiquad cascade or SVFState Variable Filter (SVF)
Shelving / high-shelf / low-shelfBiquad (Audio EQ Cookbook)Peaking EQ or shelf coefficients
Reverb (algorithmic)FDN or Schroeder/MoorerFeedback Delay Network (FDN)
Reverb (convolution / IR)OLA / OLSOverlap-Add with FFT
Compressor / limiter / expander / gateLevel detector + gain computerRMS or peak detector + knee curve
Pitch shift / time stretchPhase vocoder or granularPhase vocoder for tonal material
Anti-aliased oscillatorBLIT / PolyBLEP / wavetablePolyBLEP for simple waveforms
Spectral processing / analysisSTFT pipelineOverlap-Add / Overlap-Save
Waveshaper / saturationMemoryless nonlinearitySoft-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 double for coefficient computation; cast to float for 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.

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