analyze_decomposition_time

Overview

analyze_decomposition_time performs time-domain harmonic decomposition of ADC output, separating the fundamental from harmonic distortion components. This reveals the temporal structure of nonlinearity.

Syntax

from adctoolbox import analyze_decomposition_time

# Basic usage
result = analyze_decomposition_time(signal, fs=100e6, harmonic=5,
                                    show_plot=True)

# With custom parameters
result = analyze_decomposition_time(signal, fs=100e6, harmonic=9)

Parameters

  • signal (array_like) — Input ADC signal

  • fs (float) — Sampling frequency in Hz

  • harmonic (int, default=5) — Number of harmonics to decompose

  • show_plot (bool, default=False) — Display decomposition plot

  • ax (matplotlib axis, optional) — Axis for plotting

Returns

Dictionary containing:

  • fundamental — Fundamental component (time domain)

  • harmonics — List of harmonic components

  • residual — Remaining error (noise + distortion)

  • harmonic_amplitudes — Amplitude of each harmonic

  • harmonic_phases — Phase of each harmonic

Algorithm

# 1. Fit fundamental
result = fit_sine_4param(signal)
fundamental = result['fitted_signal']

# 2. Extract each harmonic by fitting at k×f₀
for k in range(2, harmonic + 1):
    harmonic_k = fit_sine_at_frequency(signal, freq_estimate * k)

# 3. Compute residual
residual = signal - fundamental - sum(all_harmonics)

Use Cases

  • Visualize harmonic distortion in time domain

  • Understand nonlinearity structure (2nd vs. 3rd order)

  • Compare with polar decomposition for phase insights

See Also

References

  1. IEEE Std 1057-2017, “IEEE Standard for Digitizing Waveform Recorders”