CochleagramDistance

Introduction

Cochleagram Distance is a metric designed to compare the cochleagram representations of two audio signals. The cochleagram is based on the functioning of the human cochlea and represents how sound is processed by the auditory system. This distance measure is particularly useful for applications where human perception of sound plays a critical role.

Sense of the Distance

Cochleagram Distance quantifies the dissimilarity between two signals by comparing their cochleagram representations, which capture the frequency and temporal aspects of sound as perceived by the human auditory system.

Formal Representation

The Cochleagram Distance between two signals ( x(t) ) and ( y(t) ) can be mathematically represented as: [ Cochlea_{dist}(x, y) = | Cochleagram(x) - Cochleagram(y) |_p ] where ( Cochleagram(x) ) and ( Cochleagram(y) ) represent the cochleagram transformations of the signals ( x(t) ) and ( y(t) ), respectively, and ( | cdot |_p ) denotes an appropriate distance measure (such as the L2 norm) applied to the cochleagram representations.

from distancia import CochleagramDistance

# Example usage:

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

cochleagram_calculator = CochleagramDistance(num_bands=40)

distance_value: float = cochleagram_calculator.compute(signal1, signal2)

print(“Cochleagram Distance:”, distance_value)

>>>Cochleagram Distance: 0.000833203125000008

Academic Reference

Wang[1]:

[1]

D Wang. Computational auditory scene analysis: principles, algorithms, and applications. 2006.

Conclusion

The CochleagramDistance class provides a perceptually relevant distance measure by comparing the cochleagram representations of two audio signals, making it suitable for tasks where human auditory perception is central.