35 research outputs found
Fractional order differentiation by integration with Jacobi polynomials
The differentiation by integration method with Jacobi polynomials was
originally introduced by Mboup, Join and Fliess. This paper generalizes this
method from the integer order to the fractional order for estimating the
fractional order derivatives of noisy signals. The proposed fractional order
differentiator is deduced from the Jacobi orthogonal polynomial filter and the
Riemann-Liouville fractional order derivative definition. Exact and simple
formula for this differentiator is given where an integral formula involving
Jacobi polynomials and the noisy signal is used without complex mathematical
deduction. Hence, it can be used both for continuous-time and discrete-time
models. The comparison between our differentiator and the recently introduced
digital fractional order Savitzky-Golay differentiator is given in numerical
simulations so as to show its accuracy and robustness with respect to
corrupting noises
Improved IIR Low-Pass Smoothers and Differentiators with Tunable Delay
Regression analysis using orthogonal polynomials in the time domain is used
to derive closed-form expressions for causal and non-causal filters with an
infinite impulse response (IIR) and a maximally-flat magnitude and delay
response. The phase response of the resulting low-order smoothers and
differentiators, with low-pass characteristics, may be tuned to yield the
desired delay in the pass band or for zero gain at the Nyquist frequency. The
filter response is improved when the shape of the exponential weighting
function is modified and discrete associated Laguerre polynomials are used in
the analysis. As an illustrative example, the derivative filters are used to
generate an optical-flow field and to detect moving ground targets, in real
video data collected from an airborne platform with an electro-optic sensor.Comment: To appear in Proc. International Conference on Digital Image
Computing: Techniques and Applications (DICTA), Adelaide, 23rd-25th Nov. 201
Non-asymptotic fractional order differentiators via an algebraic parametric method
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer
order differentiators by using an algebraic parametric estimation method [7],
[8]. In this paper, in order to obtain non-asymptotic fractional order
differentiators we apply this algebraic parametric method to truncated
expansions of fractional Taylor series based on the Jumarie's modified
Riemann-Liouville derivative [14]. Exact and simple formulae for these
differentiators are given where a sliding integration window of a noisy signal
involving Jacobi polynomials is used without complex mathematical deduction.
The efficiency and the stability with respect to corrupting noises of the
proposed fractional order differentiators are shown in numerical simulations
On Generalized Fractional Differentiator Signals
By employing the generalized fractional differential operator, we introduce a system of fractional order derivative for a uniformly sampled polynomial signal. The calculation of the bring in signal depends on the additive combination of the weighted bring-in of N cascaded digital differentiators. The weights are imposed in a closed formula containing the Stirling numbers of the first kind. The approach taken in this work is to consider that signal function in terms of Newton series. The convergence of the system to a fractional time differentiator is discussed
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Identification of fractional-order transfer functions using a step excitation
This brief proposes a new method for the identification
of fractional order transfer functions based on the time
response resulting from a single step excitation. The proposed method is applied to the identification of a three-dimensional RC network, which can be tailored in terms of topology and composition to emulate real time systems governed by fractional order dynamics. The results are in excellent agreement with the actual network response, yet the identification procedure only requires a small number of coefficients to be determined,
demonstrating that the fractional order modelling approach leads to very parsimonious model formulations
Aplicação de filtros de Savitzky-Golay no processamento de sinais de eletrocardiografia.
O presente trabalho é parte do projeto FINEP sob o convênio 01.13.0387, cujo objetivo global é a construção de um microssistema de eletrocardiografia de baixo custo para monitoramento remoto. Neste contexto, o objetivo específico deste trabalho é projetar filtros digitais diferenciadores, baseados na técnica dos mínimos quadrados de Savitzky-Golay, capazes de eliminar ruídos provenientes das interferências de alta frequência e também da rede elétrica, para melhorar confiabilidade das medidas, mantendo o projeto comprometido com as normas técnicas aplicáveis e com o baixo custo. As novas abordagens mantêm as mesmas propriedades da abordagem clássica, porém resultam em filtros com menor amplificação de ruído