PESQ

Introduction

The PESQ (Perceptual Evaluation of Speech Quality) class measures the quality of speech signals by comparing a degraded signal to a reference signal. This objective method is widely used in telecommunications to assess the impact of network impairments on voice quality.

Sense of the Distance

PESQ is a perceptual model that quantifies the perceived difference between two speech signals by simulating how the human ear evaluates voice quality. The closer the PESQ score is to the maximum value, the more similar the degraded signal is to the original reference signal.

Formal Representation

PESQ evaluates the perceptual difference between a reference signal ( s_{ref}(t) ) and a degraded signal ( s_{deg}(t) ), based on a model of auditory perception. The PESQ score is computed as: [ PESQ(s_{ref}, s_{deg}) = text{PESQ model output} ] where the score typically ranges from -0.5 to 4.5, with higher scores indicating better perceived quality.

from distancia import PESQ

reference_signal: List[float] = [0.1 * math.sin(2 * math.pi * 440 * t / 16000) for t in range(16000)]
degraded_signal: List[float] = [0.1 * math.sin(2 * math.pi * 440 * t / 16000) + 0.01 * math.sin(2 * math.pi * 1000 * t / 16000) for t in range(16000)]

pesq_calculator = PESQ(sample_rate=16000)

pesq_score: float = pesq_calculator.compute_pesq(reference_signal, degraded_signal)

print("PESQ Score:", pesq_score)

>>>PESQ Score: 4.492250820344904

Academic Reference

Rix et al.[1]

[1]

A.W. Rix, J.G. Beerends, M.P. Hollier, and A.P. Hekstra. Perceptual evaluation of speech quality (pesq)-a new method for speech quality assessment of telephone networks and codecs. In 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221), volume 2, 749–752 vol.2. 2001. doi:10.1109/ICASSP.2001.941023.

Conclusion

The PESQ class provides a standardized method for evaluating the perceptual quality of speech signals, making it an essential tool in the evaluation of voice codecs, telecommunication systems, and network performance.