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 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.