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Distortion and Linearity Analyzers

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youtube-at-vach edited this page Jul 23, 2026 · 1 revision

Distortion and Linearity Analyzers

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This section covers the modules and core algorithms used for quantifying non-ideal behavior in audio systems, ranging from standard harmonic distortion (THD) and intermodulation (IMD) to complex multitone analysis and amplitude-dependent gain linearity.

Distortion Analyzer

The Distortion Analyzer is the primary tool for measuring fundamental audio performance metrics including THD, THD+N, SINAD, and IMD. It supports real-time monitoring as well as automated frequency and amplitude sweeps.

Core Analysis Logic

The analyzer relies on AudioCalc.calculate_harmonic_distortion to extract metrics from a captured time-domain buffer. The process follows these steps:

  1. Fundamental Extraction: Uses a high-precision sine fit or FFT bin peak detection to identify the fundamental frequency $f_0$.
  2. Harmonic Analysis: Measures the RMS levels of $2f_0, 3f_0, \dots, Nf_0$ src/gui/widgets/distortion_analyzer.py:103-183.
  3. Residual Calculation: Subtracts the fundamental from the signal to calculate the noise and distortion residue ($THD+N$) src/core/analysis.py:270-340.
  4. Averaging: Implements a moving average using raw RMS components (raw_fund_rms, raw_res_rms) rather than averaging the final percentage values to maintain mathematical accuracy during noise floor fluctuations src/gui/widgets/distortion_analyzer.py:103-166.

Data Flow: Real-time Distortion Analysis

The following diagram illustrates the data flow from the AudioEngine through the analysis pipeline.

Distortion Analysis Pipeline

graph TD
    subgraph Audio_Input ["Audio Engine Pipeline"]
        AE["AudioEngine Callback"] --> RB["Ring Buffer (input_data)"]
    end

    subgraph Analysis_Core ["DistortionAnalyzer Analysis"]
        RB --> WIN["Apply Window (Blackman-Harris)"]
        WIN --> FFT["FFT Manager (rfft)"]
        FFT --> PK["Peak Detection (Fundamental)"]
        PK --> HARM["Harmonic Extraction (2nd-Nth)"]
        PK --> RES["Residual Calculation (Notch Fundamental)"]
    end

    subgraph Metrics_Output ["Result Generation"]
        HARM --> THD["THD Calculation"]
        RES --> THDN["THD+N / SINAD"]
        THD --> AVG["_apply_result_averaging"]
        THDN --> AVG
        AVG --> UI["Update DistortionAnalyzer UI"]
    end

    Sources["Sources: src/gui/widgets/distortion_analyzer.py:103-183, src/core/analysis.py:270-340"]
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Sources: src/gui/widgets/distortion_analyzer.py:103-183, src/core/analysis.py:270-340

Advanced Distortion Meter

The Advanced Distortion Meter handles complex stimulus signals that reveal nonlinearities not easily captured by single-tone tests.

Supported Modes

  • MIM (Multitone Intermodulation): Generates a "comb" of $N$ sine waves (typically 31 tones from 20Hz to 20kHz) with phases optimized to minimize the crest factor using Newman phases src/gui/widgets/advanced_distortion_meter.py:57-61. It measures the "grass" between tones to determine the Total Distortion Power.
  • PIM (Phase Intermodulation): Uses two closely spaced high-frequency tones to measure sideband generation caused by phase/frequency modulation in the DUT src/gui/widgets/advanced_distortion_meter.py:63-68.
  • J-Test: A specific stimulus for measuring jitter-induced distortion in digital interfaces, particularly AES3 and S/PDIF src/gui/widgets/advanced_distortion_meter.py:70-71.

Coherent Stimulus Generation

To prevent spectral leakage without requiring aggressive windowing, the AdvancedDistortionMeter uses Coherent Multitone Generation. Frequencies are snapped to exact FFT bin centers: $f_{bin} = \text{round}\left(\frac{f_{target}}{\Delta f}\right) \cdot \Delta f$ where $\Delta f = \frac{f_s}{N_{FFT}}$ src/gui/widgets/advanced_distortion_meter.py:206-215.

Sources: src/gui/widgets/advanced_distortion_meter.py:37-77, src/gui/widgets/advanced_distortion_meter.py:206-230

Linearity Analyzer

The Linearity Analyzer measures gain stability relative to signal amplitude. This is critical for detecting compression, expansion, or crossover distortion in amplifiers and DACs.

Implementation: LinearitySweepWorker

The measurement is performed by a dedicated LinearitySweepWorker thread:

  1. Stimulus: Steps the SignalGenerator amplitude through a range (e.g., 0 dBFS down to -120 dBFS) src/gui/widgets/linearity_analyzer.py:119-138.
  2. Lock-in Detection: Uses AudioCalc.calculate_lockin_measurement at each step to extract the magnitude of the test frequency with extremely high narrow-band rejection src/gui/widgets/linearity_analyzer.py:196-198.
  3. Hysteresis Analysis: If enabled, the worker performs a bi-directional sweep (Low $\to$ High $\to$ Low). The function calculate_hysteresis compares the gain at identical amplitude points to detect thermal or memory effects in the DUT src/gui/widgets/linearity_analyzer.py:30-96.

Linearity Measurement Logic

graph LR
    subgraph Stimulus ["Stimulus Generation"]
        GEN["SignalGenerator"] -- "Set Amplitude" --> DUT["Device Under Test"]
    end

    subgraph Processing ["LinearitySweepWorker"]
        DUT --> BUF["Get Latest Buffer"]
        BUF --> LOCK["AudioCalc.calculate_lockin_measurement"]
        LOCK --> MAG["Extract Magnitude"]
        MAG --> CALC["Calculate Deviation from Ref Gain"]
    end

    subgraph Results ["Result Output"]
        CALC --> PLOT["Plot Linearity (dB vs dBFS)"]
        CALC --> HYST["calculate_hysteresis"]
    end

    Sources["Sources: src/gui/widgets/linearity_analyzer.py:30-96, src/gui/widgets/linearity_analyzer.py:157-210"]
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Sources: src/gui/widgets/linearity_analyzer.py:30-96, src/gui/widgets/linearity_analyzer.py:99-210

Core Algorithms (analysis.py)

The analysis.py module provides the mathematical foundation for all distortion and linearity metrics.

Weighting Filters

Weighting filters are implemented as Second-Order Sections (SOS) to ensure numerical stability at high sampling rates.

  • A-Weighting: Implemented based on IEC 61672:2003 poles and zeros src/core/analysis.py:15-26.
  • Weighting Application: The _calculate_ra_raw function computes the analog response curve, which is then mapped to the digital domain using the bilinear transform or frequency-domain multiplication for FFT-based analysis src/core/analysis.py:45-55.

Precision Frequency Tracking

For modules like the Frequency Counter and 1PPS Monitor, high-precision frequency estimation is required:

  • Sine Fitting: Uses a four-parameter sine fit (amplitude, frequency, phase, DC offset) to estimate the signal parameters beyond FFT bin resolution src/core/analysis.py:343-410.
  • Online Regression: The OnePPSMonitor uses an Online Least Squares Regression to track sample clock drift (PPM) over time without storing the entire history in memory src/gui/widgets/one_pps_monitor.py:78-87.

Table: Key Analysis Functions

Function File Description
calculate_harmonic_distortion analysis.py Extracts THD, THD+N, and individual harmonics.
calculate_lockin_measurement analysis.py Dual-phase demodulation for linearity and impedance.
calculate_noise_profile analysis.py Computes PSD, 1/f noise, and integrated noise floor.
calculate_allan_deviation frequency_analysis.py Statistical measure of frequency stability.

Sources: src/core/analysis.py:15-55, src/core/analysis.py:343-410, src/gui/widgets/one_pps_monitor.py:78-87

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