A catalogue of the named DSP, mathematical and estimation algorithms
used across Phonalyser.web's modules - what each one is, where this help
explains it, and where to read the theory. This page is the condensed
view of the project's full engineering document
ALGORITHMS.md[1],
which carries the per-algorithm mathematics and source citations.
| Algorithm | What it does here | In this help |
|---|
| Direct digital synthesis (DDS) |
64-bit phase-accumulator oscillator; exact mod-2⁶⁴ phase,
click-free frequency changes, picohertz-class trim
granularity. |
Generator - phase accumulator |
| Angle-sum + Taylor sine |
4096-entry table for the coarse angle plus a 5th-order Taylor
series for the remainder - an exact sine without per-sample
trigonometric library calls. |
Generator - sine kernel |
| Farina exponential sine sweep |
Log-chirp probe with equal energy per octave; pre-rendered so
the deconvolution reference equals the played signal. |
Generator - sweeps,
Frequency response |
| Voss-McCartney pink noise |
Summed-octave 1/f generator, constant cost per sample. |
Generator - noise |
| TPDF dither |
Triangular-PDF dither before quantization; decorrelates the
rounding error from the signal. |
Generator - quantization |
| Raised-cosine (Hann) taper |
Sweep fade-in/out; suppresses start/stop spectral leakage. |
Generator - sweeps |
| Algorithm | What it does here | In this help |
|---|
| Radix-2 Cooley-Tukey FFT |
The transform itself - in-place, parallelised at large sizes
(up to 4M points). |
FFT - resolution |
| Goertzel single-bin DFT |
Magnitude/phase at one arbitrary frequency in a single O(N)
pass - the engine behind the scope's millihertz frequency
readout, the mains tracker and the FFT's κ refit. |
Oscilloscope - frequency |
| Window functions (Hann, Blackman-Harris, flat-top, HFT,
Kaiser, Dolph-Chebyshev) |
Leakage control from everyday (Hann) to side-lobe floors below
anything a physical converter produces (DC300, KB38). |
FFT - windows |
| Phase-difference sub-bin estimator |
The tone's fractional bin κ from the phase advance between
blocks - far finer than any magnitude peak-pick. |
FFT - sub-bin frequency |
| Parabolic peak interpolation |
Three-point quadratic fit for sub-bin peaks; the fallback κ
estimator and the IMD tone-level refiner. |
FFT - sub-bin frequency |
| Coherent (vector) averaging with per-lobe de-rotation |
Phase-aligned complex averaging - the noise floor falls
10·log₁₀M dB while tones stand still. |
FFT - coherent averaging;
De-rotation accuracy
(error budget) |
| Intermodulation product grid |
Two-tone products a·f₁+b·f₂ de-rotated at their true
frequencies; CCIF/DIN difference-frequency ratios. |
FFT - two-tone |
| Median + MAD robust statistics |
Self-calibrating thresholds for the noise floor and the
spectral glitch gates - learned from the data, immune to
outliers. |
FFT - glitch rejection |
| Tone-lobe stretch (ToneLobeLift) |
Rescales a tone's main lobe as a vertical stretch pinned to the
noise floor - a smooth dome, never a flat-topped uniform lift -
for .frc calibration and manual-fundamental
levelling. |
- (spectral rendering; see the full
document[1]) |
| Algorithm | What it does here | In this help |
|---|
| Lanczos (windowed-sinc) interpolation |
Band-limited reconstruction of the trace between samples -
the scope's zoomed-in rendering and sub-sample trigger
refinement. |
Oscilloscope - pipeline |
| Schmitt trigger (hysteresis) |
Dual-threshold edge qualification so noise riding on the
signal can't double-fire the trigger. |
Oscilloscope - trigger |
| Sinusoid-recurrence discontinuity detector |
Predicts each sample from the two before it via the tone's own
recurrence di ≈ 2 cos ω ·
di−1 − di−2; the prediction
error sits at the noise floor on a clean signal and jumps decades
above an 8×-mean threshold at any splice or dropout - the scope's
glitch trigger and the FFT's time-domain capture gate share the
same detector, so both agree on what counts as damage. |
Oscilloscope - trigger |
| Chebyshev IIR low-pass + median de-spike |
High-frequency spike removal on the display path only - the
measurement pass takes the captured window, mains comb aside. |
Oscilloscope -
conditioning |
| Frequency-tracked IIR comb |
One filter notching the mains fundamental and every harmonic,
re-tuned as the line drifts; applied in the time domain on the
scope, as a plot-time spectral correction in the FFT. |
Oscilloscope - mains comb |
| Adaptive mains cancellers (LMS, synchronous subtraction) |
Two selectable alternatives to the comb: an LMS line canceller
with per-harmonic quadrature weights, and a period-locked 512-bin
template subtractor - both learn the hum and leave non-periodic
test tones untouched. A shared Goertzel tracker auto-detects
50 vs 60 Hz. |
Oscilloscope - mains rejection |
| Synchronous I/Q (lock-in) detection |
Recovers the dual-tone beat envelope's phase so the trigger
locks once per beat. |
Oscilloscope - trigger |
| Frequency-domain deconvolution H = Y/X |
The whole transfer function - magnitude and phase - from one
sweep. |
Frequency response |
| Looping circular-transform deconvolution |
Forces the sweep period to a power of two so the FFT is
circular - a window grabbed at any phase is a shift, and a shift
preserves |H| - giving trigger-free live notch tracking, a few
times a second, in the tune-notch wizard. |
Tune-notch measurement |
| Linear-phase delay rotation |
Removes the DAC↔ADC round-trip delay so only the device's own
phase remains. |
Frequency response -
corrections |
| Savitzky-Golay smoothing |
Sliding polynomial fit - smooths measurement ripple while
preserving notches and resonances. |
Frequency response -
corrections |
| RIAA / IEC equalisation curves |
Analytic 3180/318/75 µs (+7950 µs IEC) phono curve for overlay
and compare-mode subtraction. |
Frequency response -
calibration |
| Frequency-lock loop (FLL) |
Steers the generator onto the FFT bin grid with deadbeat
corrections, exact transport bookkeeping and drift
feedforward - sub-ppb steady-state alignment. |
Generator - phase accumulator,
FFT - integration |
| Algorithm | What it does here | In this help |
|---|
| Welford's online variance |
One-pass mean and σ for the live measurement statistics
table. |
Oscilloscope -
measurements |
| Whole-period Vmean/Vrms integration |
Integrates over an integer number of signal periods, so the
partial-cycle remainder - a reading scatter that grows with
amplitude - drops out of the mean and RMS. |
Oscilloscope -
measurements |
| Exponential moving average |
Smooths the live sweep meter and the mains-lock detections. |
Oscilloscope - mains comb |
| Liang-Barsky line clipping, 1-2-5 "nice" axis ticks,
min/max column decimation |
The shared chart engine: clipped polylines (million-bin spectra
in bounded time), readable axis labelling, per-pixel envelope
bars for dense data. |
- (rendering internals; see the full
document[1]) |
| Digital-phosphor persistence |
Oscilloscope-style afterglow on the GPU trace path: an RGBA16F
framebuffer decayed by exp(−dt/τ) on each new frame, with
off / fixed / infinite / manual time constants. |
- (GPU rendering; see the full
document[1]) |
| Algorithm | What it does here | In this help |
|---|
| Code-density histogram |
Bins every captured sample by its ADC code (2bits
bins) and compares the counts against an ideal density - a
moving-average/FIR reference, or the arcsine law of a known
sine - to expose converter linearity. Not the oscilloscope's
amplitude histogram: that
one bins by voltage over a signal-sized range to
characterise the signal, this one bins by code over the
whole converter range to characterise the converter. |
- (command-line mode; see the full
document[1]) |
| DNL / INL (code-density test) |
Differential nonlinearity DNL = weight − 1 and its running
integral INL, in LSB, straight from the histogram counts. |
- (command-line mode; see the full
document[1]) |
| Least-squares sine-fit calibration |
Recovers amplitude, phase, DC and a per-code error curve directly
from the raw samples via a golden-section frequency search and a
3×3 normal-equation sine fit - for when histogram binning is too
noisy. |
- (command-line mode; see the full
document[1]) |
Going deeper. Every entry above is treated in
full - with the equations, the parameter values and `file:line`
citations into the source - in the repository document
doc/ALGORITHMS.md[1].
The build can also render it to PDF (see
BUILD.md in the
repository).