Cepstrum Analysis

Manuale tecnico completo

Purpose

The module computes the real cepstrum of one uniformly sampled signal and exposes the result as normal GX-TXT data.

For a windowed signal x[n], the implemented definition is:

c[n] = real(IFFT(log(max(abs(FFT(x[n] w[n])), magnitude_floor))))

The horizontal coordinate is quefrency in seconds. A periodic harmonic spacing in the spectrum can produce a cepstral peak near the corresponding time period.

Input

• Contract: timeseries.table
• Independent binding: a time-compatible variable
• Signal binding: one measured numeric variable

The current release requires uniform sampling. Explicit time coordinates are accepted when their interval is uniform within the runtime tolerance.

Configuration

• Analysis window: rectangular, Hann, Hamming, Blackman-Harris, or flat-top
• Detrend: none, mean, or linear
• Log-magnitude floor in dB relative to the spectral maximum
• Minimum and maximum fundamental search frequency
• Output Dataset ID

The frequency search range is converted to the equivalent positive-quefrency range. The strongest cepstral peak inside that range is reported as the dominant periodicity.

Output

The derived table.generic Dataset contains:

quefrency_s
real_cepstrum

The module also writes:

cepstrum_metrics.ini
cepstrum_report.txt
render_cache.mat
01_real_cepstrum.png

Graph variants use the cached scientific result and do not rerun the transform.

Interpretation

A detected cepstral peak is evidence of periodic structure in the log-magnitude spectrum; it is not automatically proof of a unique physical fundamental. Peaks may also occur at multiples of the fundamental period. The configured search interval therefore remains part of the scientific method and is stored in the report/provenance.

The zero-quefrency term depends strongly on absolute amplitude scaling and the logarithm convention. Non-zero quefrency structure is the main scientific output.

Relationship to other GX-TXT modules

• analysis.fft_spectrum: conventional single-signal spectrum and established spectral metrics
• analysis.time_dependent_fft: time-dependent FFT/STFT-style analysis
• analysis.welch_spectrum: averaged spectrum/PSD
• analysis.cross_spectral_transfer: transfer/coherence analysis
• analysis.fractional_octave_spectrum: fractional-octave band integration
• analysis.harmonic_analysis: explicit integer-harmonic table and THD from an existing spectrum
• analysis.cepstrum: periodicity in log-spectral structure

Limitations

Version 1.1.1 implements the real cepstrum only. Complex cepstrum, phase unwrapping, minimum-phase reconstruction, speech-specific pitch tracking, and time-varying cepstral analysis are outside this release.

Public GX-TXT APIs used

Analysis Source Map, Dataset Variable Schema, Table Stream, Dataset Publication v2, Progress, Graph Provider, Plot Module, Unit Registry, Plugin Install, Session Generator Library, and Documentation APIs.

Shared numerical and graphics services

Version 1.1.1 uses public NUMERIC_API_v1 for grid validation, FFT, IFFT, detrending, reusable analysis-window generation and polynomial peak refinement. The numerical service is resolved from public dependency metadata injected into the Standard Module runtime configuration; the module does not depend on the physical math.numeric installation path. The module retains only cepstrum-specific logarithmic-spectrum, quefrency and peak-interpretation semantics. Scientific result graphics use persistent plot.dataset / PLOT_DATASET_API_v2.