dsp-algorithm-guide

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.