BarkSpectralDistortion

Introduction

The BarkSpectralDistortion (BSD) class is based on the Bark scale, which approximates human auditory perception of frequency. It measures the distortion between two signals by comparing their frequency content within critical bands defined by the Bark scale.

Sense of the Distance

Bark Spectral Distortion quantifies how similar or different two signals are in terms of their perceived frequency content, taking into account the non-linear way in which humans perceive sound frequencies. It is commonly used in audio coding, compression, and quality assessment.

Formal Representation

The Bark Spectral Distortion between two signals ( x(t) ) and ( y(t) ) can be represented as: [ BSD(x, y) = sum_{b=1}^{B} left( S_x(b) - S_y(b) right)^2 ] where ( S_x(b) ) and ( S_y(b) ) are the power spectral densities of signals ( x(t) ) and ( y(t) ) in the Bark frequency band ( b ), and ( B ) is the total number of Bark bands.

from distancia import BarkSpectralDistortion

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 * 445 * t / 16000) for t in range(16000)]  # Slightly different frequency

bsd_calculator = BarkSpectralDistortion(sample_rate=16000)

bsd_value: float = bsd_calculator.compute_bsd(signal1, signal2)

print("Bark Spectral Distortion:", bsd_value)

>>>Bark Spectral Distortion: 14.65614015181136

Academic Reference

Zwicker and Terhardt[1]:

[1]

Eberhard Zwicker and Ernst Terhardt. Analytical expressions for critical-band rate and critical bandwidth as a function of frequency. The Journal of the Acoustical Society of America, 68(5):1523–1525, 1980.

Conclusion

The BarkSpectralDistortion class provides an efficient method for evaluating signal differences in a way that mirrors human auditory perception, making it particularly useful in audio signal processing and evaluation tasks.