Mathematical Representation for speech signal based on ‎polynomial equation

Entesar Alasaad, Khalil I. Alsaif


The sound is an important vital information that it relies to recognize the character when lessening to it. Therefore, the audio signal adopted into many important applications. Sound forming and synthesizing in addition to distinguishing the speaker are so important in fields of digital signal processing. In this paper, work is done to represent acquired acoustic signal based on mathematical techniques. Mathematical representation provides  deal with the sound signal which lead to smoothing, amplification or compression, in addition to the sound filtering process. In the proposed algorithm, polynomials of various degrees were adopted as a mathematical representation for speech signal, then the retrieved speech was studied based on level of clarity and the possibility of adopting it as an alternative signal in terms of the proximity to the original sound and the amount of noise added to it.  The results shows that the proposed algorithm with degree of polynomial 20 and segment length 25 had the best sound representation and so closed to the original, which clearly seen from the evaluation parameters (Correlation=0.9993, Mean squared error(MSE) =1.32e-06, Standard deviation(STD)=1.80e-05 and the Euclidean dimension(ED) =0.1703).


curve fitting, sound representation, digital speech processing, digital signal processing.

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