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Fractional Linear Prediction Toolbox for MATLAB Despotovic, Vladimir ; in Proc. of 21th International Carpathian Control Conference (ICCC) (2020, October) This paper presents the Fractional Linear Prediction (FLP) Toolbox implemented in MATLAB with a supporting livescript interface that offers an user-friendly environment for the prediction of one ... [more ▼] This paper presents the Fractional Linear Prediction (FLP) Toolbox implemented in MATLAB with a supporting livescript interface that offers an user-friendly environment for the prediction of one-dimensional signals. Two versions of the FLP are implemented in the toolbox and presented here. While the first approach is using the “full” memory (the whole history of the signal), the second approach uses the “restricted” memory (two, three or four previous samples). Both FLP approaches are compared to the standard linear prediction and their performance is evaluated in examples using a test signal (sine wave signal), and a real-data signal (speech signal) as the input. [less ▲] Detailed reference viewed: 96 (2 UL)Speech Based Estimation of Parkinson’s Disease Using Gaussian Processes and Automatic Relevance Determination Despotovic, Vladimir ; ; Schommer, Christoph in Neurocomputing (2020), 401 Parkinson’s disease is a progressive neurodegenerative disorder often accompanied by impairment in articulation, phonation, prosody and fluency of speech. In fact, speech impairment is one of the earliest ... [more ▼] Parkinson’s disease is a progressive neurodegenerative disorder often accompanied by impairment in articulation, phonation, prosody and fluency of speech. In fact, speech impairment is one of the earliest Parkinson’s disease symptoms, and may be used for early diagnosis. We present an experimental study of identification of Parkinson’s disease and assessment of disease progress from speech using Gaussian processes, which is further combined with Automatic Relevance Determination (ARD) for efficient feature selection. Hyperparameters of ARD covariance functions are learned for each individual feature; therefore, can be used for evaluation of their importance. In that way only a small subset of highly relevant acoustic features is selected, leading to models with better performance and lower complexity. The performance of the proposed method was assessed on two datasets: Parkinson’s disease detection dataset, which contains a range of biomedical voice measurements obtained from 31 subjects, 23 of them suffering from Parkinson’s disease and 8 healthy subjects; and Parkinson’s telemonitoring dataset, containing biomedical voice measurements collected from 42 Parkinson’s disease patients for estimation of the disease progress. Gaussian process classification with automatic relevance determination is able to successfully discriminate between Parkinson’s disease patients and healthy controls with 96.92% accuracy, outperforming Support Vector Machines and decision tree ensembles (random forests, boosted and bagged decision trees). The usability of Gaussian processes is further confirmed in regression task for tracking the progress of the disease. [less ▲] Detailed reference viewed: 96 (8 UL)Two-dimensional fractional linear prediction ; Despotovic, Vladimir ; in Computers and Electrical Engineering (2019), 77 Linear prediction (LP) has been applied with great success in coding of one-dimensional, time-varying signals, such as speech or biomedical signals. In case of two-dimensional signal representation (e.g ... [more ▼] Linear prediction (LP) has been applied with great success in coding of one-dimensional, time-varying signals, such as speech or biomedical signals. In case of two-dimensional signal representation (e.g. images) the model can be extended by applying one-dimensional LP along two space directions (2D LP). Fractional linear prediction (FLP) is a generalisation of standard LP using the derivatives of non-integer (arbitrary real) order. While FLP was successfully applied to one-dimensional signals, there are no reported implementations in multidimensional space. In this paper two variants of two-dimensional FLP (2D FLP) are proposed and optimal predictor coefficients are derived. The experiments using various grayscale images confirm that the proposed 2D FLP models are able to achieve comparable performance in comparison to 2D LP using the same support region of the predictor, but with one predictor coefficient less, enabling potential compression. [less ▲] Detailed reference viewed: 49 (9 UL)Audio signal processing using fractional linear prediction ; Despotovic, Vladimir in Mathematics (2019), 7(7), Fractional linear prediction (FLP), as a generalization of conventional linear prediction (LP), was recently successfully applied in different fields of research and engineering, such as biomedical signal ... [more ▼] Fractional linear prediction (FLP), as a generalization of conventional linear prediction (LP), was recently successfully applied in different fields of research and engineering, such as biomedical signal processing, speech modeling and image processing. The FLP model has a similar design as the conventional LP model, i.e., it uses a linear combination of “fractional terms” with different orders of fractional derivative. Assuming only one “fractional term” and using limited number of previous samples for prediction, FLP model with “restricted memory” is presented in this paper and the closed-form expressions for calculation of FLP coefficients are derived. This FLP model is fully comparable with the widely used low-order LP, as it uses the same number of previous samples, but less predictor coefficients, making it more efficient. Two different datasets, MIDI Aligned Piano Sounds (MAPS) and Orchset, were used for the experiments. Triads representing the chords composed of three randomly chosen notes and usual Western musical chords (both of them from MAPS dataset) served as the test signals, while the piano recordings from MAPS dataset and orchestra recordings from the Orchset dataset served as the musical signal. The results show enhancement of FLP over LP in terms of model complexity, whereas the performance is comparable. [less ▲] Detailed reference viewed: 84 (7 UL)Optimal fractional linear prediction with restricted memory ; Despotovic, Vladimir ; in IEEE Signal Processing Letters (2019), 26(5), 760-764 Linear prediction is extensively used in modeling, compression, coding, and generation of speech signal. Various formulations of linear prediction are available, both in time and frequency domain, which ... [more ▼] Linear prediction is extensively used in modeling, compression, coding, and generation of speech signal. Various formulations of linear prediction are available, both in time and frequency domain, which start from different assumptions but result in the same solution. In this letter, we propose a novel, generalized formulation of the optimal low-order linear prediction using the fractional (non-integer) derivatives. The proposed fractional derivative formulation allows for the definition of predictor with versatile behavior based on the order of fractional derivative. We derive the closed-form expressions of the optimal fractional linear predictor with restricted memory, and prove that the optimal first-order and the optimal second-order linear predictors are only its special cases. Furthermore, we empirically prove that the optimal order of fractional derivative can be approximated by the inverse of the predictor memory, and thus, it is a priori known. Therefore, the complexity is reduced by optimizing and transferring only one predictor coefficient, i.e., one parameter less in comparison to the second-order linear predictor, at the same level of performance. [less ▲] Detailed reference viewed: 48 (7 UL)Signal prediction using fractional derivative models ; Despotovic, Vladimir in Bǎleanu, Dumitru; Mendes Lopes, António (Eds.) Handbook of Fractional Calculus with Applications (2019) In this chapter the linear prediction (LP) and its generalisation to fractional linear prediction (FLP) is described with the possible applications to one-dimensional (1D) and two-dimensional (2D) signals ... [more ▼] In this chapter the linear prediction (LP) and its generalisation to fractional linear prediction (FLP) is described with the possible applications to one-dimensional (1D) and two-dimensional (2D) signals. Standard test signals, such as the sine wave, the square wave, and the sawtooth wave, as well as the real-data signals, such as speech, electrocardiogram and electroencephalogram are used for the numerical experiments for the 1D case, and grayscale images for the 2D case. The 1D FLP model is proposed to have a similar construction as the LP model, i.e. it uses linear combination of fractional derivatives with different values of the fractional order. The 2D FLP model uses linear combination of the fractional derivatives in two directions, horizontal and vertical. The scheme for the computation of the optimal predictor coefficients for both 1D and 2D FLP models is also provided. The performance of the proposed FLP models is compared to the performance of the LP models, confirming that the proposed FLP can be successfully applied in processing of 1D and 2D signals, giving comparable or better performance using the same or even smaller number of parameters. [less ▲] Detailed reference viewed: 63 (10 UL)One-parameter fractional linear prediction Despotovic, Vladimir ; ; in Computers and Electrical Engineering (2018), 69 The one-parameter fractional linear prediction (FLP) is presented and the closed-form expressions for the evaluation of FLP coefficients are derived. Contrary to the classical first-order linear ... [more ▼] The one-parameter fractional linear prediction (FLP) is presented and the closed-form expressions for the evaluation of FLP coefficients are derived. Contrary to the classical first-order linear prediction (LP) that uses one previous sample and one predictor coefficient, the one-parameter FLP model is derived using the memory of two, three or four samples, while not increasing the number of predictor coefficients. The first-order LP is only a special case of the proposed one-parameter FLP when the order of fractional derivative tends to zero. Based on the numerical experiments using test signals (sine test waves), and real-data signals (speech and electrocardiogram), the hypothesis for estimating the fractional derivative order used in the model is given. The one-parameter FLP outperforms the classical first-order LP in terms of the prediction gain, having comparable performance with the second-order LP, although using one predictor coefficient less. [less ▲] Detailed reference viewed: 58 (2 UL)Linear prediction of speech: The fractional derivative formula Despotovic, Vladimir ; in Book of Abstracts, 2017 International Workshop on Fractional Calculus and Its Applications (2017, May) Detailed reference viewed: 40 (1 UL)Fractional-order speech prediction Despotovic, Vladimir ; in International Conference on Fractional Differentiation and its Applications (ICFDA ‘16) (2016, July) Detailed reference viewed: 43 (1 UL)Identification of systems of arbitrary real order: a new method based on systems of fractional order differential equations and orthogonal distance fitting ; Despotovic, Vladimir in Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C (2009, September) A new method for identification of systems of arbitrary real order based on numerical solution of systems of nonlinear fractional order differential equations (FODEs) and orthogonal distance fitting is ... [more ▼] A new method for identification of systems of arbitrary real order based on numerical solution of systems of nonlinear fractional order differential equations (FODEs) and orthogonal distance fitting is presented. The main idea is to fit experimental or measured data using a solution of a system of fractional differential equations. The parameters of these equations, including the orders of derivatives, are subject to optimization process, where the criterion of optimization is the minimal sum of orthogonal distances of the data points from the fitting line. Once the minimal sum is found, the identified parameters are considered as optimal. The so called orthogonal distance fitting, known also under the names of total least squares or orthogonal regression is naturally used in the fitting criterion, since it is the most suitable tool for fitting lines and surfaces in multidimensional space. The examples illustrating the methods are presented in 2-dimensional and 3-dimensional problems. [less ▲] Detailed reference viewed: 54 (2 UL)Shadows on the Walls: Geometric Interpretation of Fractional Integration ; Despotovic, Vladimir ; et al in Journal of Online Mathematics and its Applications (2007), 7 In 2001/2002, Podlubny suggested a solution to the more than 300-years old problem of geometric interpretation of fractional integration (i.e., integration of an arbitrary real order). His geometric ... [more ▼] In 2001/2002, Podlubny suggested a solution to the more than 300-years old problem of geometric interpretation of fractional integration (i.e., integration of an arbitrary real order). His geometric interpretation for left-sided and right-sided Riemann-Liouville fractional integrals, and for Riesz potential is given in terms of changing time scale with constant order of integration, and also in a case of varying order of integration with constant time parameter. In this article we present animations of such interpretation. [less ▲] Detailed reference viewed: 55 (1 UL) |
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