PhaseDifferenceCalculator¶

Introduction¶

The PhaseDifferenceCalculator class computes the phase difference between two signals. Phase difference is a key concept in signal processing, especially when analyzing the relationship between periodic signals or signals in the frequency domain.

Sense of the Distance¶

The phase difference measures the relative shift in phase between two signals at a given frequency or across multiple frequencies. It captures the alignment of the signals in terms of their periodic oscillations, and can be used to understand how signals are out of sync or phase-shifted.

Formal Representation¶

Given two signals ( x(t) ) and ( y(t) ), their phase difference ( Deltaphi(f) ) at a frequency ( f ) can be represented as: [ Deltaphi(f) = phi_y(f) - phi_x(f) ] where ( phi_x(f) ) and ( phi_y(f) ) represent the phase angles of the respective signals at frequency ( f ).

The phase difference is typically calculated after transforming the signals into the frequency domain, often using the Fourier transform. The result is expressed in radians or degrees.

from distancia import PhaseDifferenceCalculator

# Paramètres
sample_rate: int = 44100  # Hz
window_size: int = 1024   # échantillons
hop_size: int = 512       # échantillons

# Créer une instance du calculateur
calculator: PhaseDifferenceCalculator = PhaseDifferenceCalculator(sample_rate, window_size, hop_size)

# Supposons que nous ayons deux signaux signal1 et signal2
signal1: List[float] = [0.1 * math.sin(2 * math.pi * 440 * t / 16000) for t in range(16000)]
signal2: List[float] = [0.1 * math.sin(2 * math.pi * 880 * t / 16000) for t in range(16000)]

# Analyser les signaux
phase_differences: List[float]
time_axis: List[float]
phase_differences, time_axis = calculator.analyze_signals(signal1, signal2)

# Afficher les résultats
print("Différences de phase:", phase_differences[:10])  # Affiche les 10 premières valeurs
print("Axe temporel:", time_axis[:10])  # Affiche les 10 premières valeurs

>>>Différences de phase: [-2.4222941361062844e-13, -3.913015744760884e-14, -8.194330630706403e-13, -0.0030679615760171794, -0.003067961575875389, -0.0030679615775843837, -0.0030679615747780456, -0.003067961575879634, -0.0030679615761320207, 1.4784289244229587e-12]

Axe temporel: [0.0]

Academic Reference¶

Bracewell and Kahn[1]

Conclusion¶

The PhaseDifferenceCalculator class allows for a precise analysis of phase shifts between two signals. This tool is particularly useful in fields such as telecommunications, audio processing, and any domain where understanding the timing relationship between periodic signals is important.