Estimation of the Fundamental Frequency of the Speech Signal Compressed by MP3 Algorithm

Milivojević, Zoran N.; Brodić, Darko

doi:10.2478/aoa-2013-0043

Cited by 5 publications

(7 citation statements)

References 34 publications

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“…The possibility of optimization of the two parameters provided greater possibilities of adaptation of the 2P kernel to specific signals. Examples of estimating the fundamental frequency, F 0 , of a speech signal, by interpolation in the spectral domain, are presented in (Milivojević & Brodić, 2013) and (Milivojević et al, 2017). As a measure of the error estimate of the fundamental frequency MSE was used.…”

Section: Introductionmentioning

confidence: 99%

Optimization of the 2P fifth degree convolution kernel in the spectral domain

Savić,

Milivojević,

Prlinčević

2023

Bull Nat Sci Research

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The first part of the paper describes a two-parameter (2P) fifth-order interpolation kernel, r. After that, from the 2P kernel, the kernel components were created. By applying the Fourier transformation to each kernel component, the spectral components of the 2P kernel were obtained. The spectral characteristic of the 2P kernel, H, was created from the spectral components. After that, the algorithm, that optimizes the parameters of the 2P kernel so as to eliminate the ripple of the spectral characteristics, is described. The optimization was performed in such a way that the spectral characteristic developed in the Taylor series, H T. With the condition for the elimination of the members of the Tylor series, which greatly affect the ripple of the spectral characteristic, the optimal kernel parameters (a opt , b opt) were determined. The second part of the paper describes an Experiment, in which the interpolation accuracy of the 2P kernel was tested. Convolution interpolation, with the 2P kernel, was performed over the signals from the Test base. The Test base is created with musical signals. By analyzing the interpolation error, which is represented by the Mean Square Error, MSE, the precision of the interpolation was determined. The results (a opt , b opt , MSE min) are presented on tables and graphs. Detailed comparative analysis showed higher interpolation precision with the proposed 2P interpolation kernel, compared to the interpolation precision with, 1P interpolation kernel. Finally, the numerical values of the optimal kernel parameters, which are determined by the optimization algorithm proposed in this paper, were experimentally verified.

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Section: Introductionmentioning

confidence: 99%

Optimization of the 2P fifth degree convolution kernel in the spectral domain

Savić,

Milivojević,

Prlinčević

2023

Bull Nat Sci Research

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show abstract

“…In the scientific literature, this kernel is called the 2P Keys kernel. Optimal values of kernel parameters (αopt = 0.1, βopt = 0.2975) in estimating the fundamental frequency of the speech signal determined in [14]. Further expansion of parameterization, in order to improve the characteristics of the kernel, led to the construction of 3P Keys kernel [15].…”

Section: Introductionmentioning

confidence: 99%

Optimization of the 3p keys kernel parameters by minimizing the ripple of the spectral characteristic

2022

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The ideal interpolation kernel is described by the sinc function, and its spectral characteristic is the box function. Due to the infinite length of the ideal kernel, it is not achievable. Therefore, convolutional interpolation kernels of finite length, which should better approximate the ideal kernel in a specified interval, are formed. The approximation function should have a small numerical complexity, so as to reduce the interpolation execution time. In the scientific literature, great attention is paid to the polynomial kernel of the third order. However, the time and spectral characteristic of the third-order polynomial kernels differs significantly from the shape of the ideal kernel. Therefore, the accuracy of cubic interpolation is lower. By optimizing the kernel parameters, it is possible to better approximate the ideal kernel. This will increase the accuracy of the interpolation. The first part of the paper describes a three-parameter (3P) Keys interpolation kernel, r. After that, the algorithm for optimizing the parameters of the 3P Keys kernel, is shown. First, the kernel is disassembled into components, and then, over each kernel component, Fourier transform is applied. In this way the spectral characteristic of the 3P Keys kernel, H, was determined. Then the spectral characteristic was developed in the Taylor series, HT. With the condition for the elimination of the members of the Taylor series, which greatly affect the ripple of the spectral characteristic, the optimal kernel parameters (?opt, ?opt, gopt) were determined. The second part of the paper describes an experiment, in which the interpolation accuracy of the 3P Keys kernel, was tested. Parametric cubic convolution (PCC) interpolation, with the 3P kernel, was performed over the images from the Test database. The Test database is created with standard Test images, which are intensively used in Digital Image Processing. By analyzing the interpolation error, which is represented by the Mean Square Error, MSE, the accuracy of the interpolation was determined. The results (?opt, ?opt, gopt, MSEmin) are presented on tables and graphs. Detailed comparative analysis showed higher interpolation accuracy with the proposed 3P Keys interpolation kernel, compared to the interpolation accuracy with, 1P Keys and 2P Keys interpolation kernels. Finally, the numerical values of the optimal kernel parameters, which are determined by the optimization algorithm proposed in this paper, were experimentally verified.

show abstract

“…In the scientific literature, this kernel is called the 2P Keys kernel. Optimization of the 2P Keys kernel parameters in the estimation of the fundamental frequency, F 0 , of the speech signal was determined in (Milivojević & Brodić, 2013) and (Milivojević et al, 2017). As a measure of the error estimate of the fundamental frequency MSE was used.…”

Section: Introductionmentioning

confidence: 99%

Spectral characteristics of two parameter fifth degree polynomial convolution kernel

Milivojević

Savić

Prlinčević

2022

Bull Nat Sci Research

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In this paper, the spectral characteristic of a polynomial two parameter convolutional fifth - order interpolation kernel is determined. The spectral characteristic is determined as follows. First, the kernel is decomposed into components. After that, the spectral characteristics of each kernel component were calculated using the Fourier transform. Finally, the spectral characteristic of the interpolation two parameter kernel using a combination of the spectral components of the kernels and the kernel parameters, α and β, is formed. Through a numerical example and a graphical representation of the spectral characteristics of the one parameter and two parameter kernels, greater similarity of the spectral characteristics of the 2 P kernel, relative to the ideal box characteristic, is shown.

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Estimation of the Fundamental Frequency of the Speech Signal Compressed by MP3 Algorithm

Cited by 5 publications

References 34 publications

Optimization of the 2P fifth degree convolution kernel in the spectral domain

Optimization of the 2P fifth degree convolution kernel in the spectral domain

Optimization of the 3p keys kernel parameters by minimizing the ripple of the spectral characteristic

Spectral characteristics of two parameter fifth degree polynomial convolution kernel

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