Abstract
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 ofNcascaded 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.
Highlights
Nowadays, fractional calculus arises in signal processing and image possessing
By using the generalized Srivastava-Owa fractional differential operator [12], we introduce a system of generalized fractional order derivative for a uniformly sampled polynomial signal
For α = 1 and any value of μ the system is a maximally linear differentiator (Figure 5). It follows from the relation (21) that the input/output characterizes the ideal digital differentiator, for fractional and integer values of α with the help of the fractional value of μ, of the polynomial signal
Summary
Fractional calculus (integral and differential operators) arises in signal processing and image possessing. Fractional calculus is employed in image retrieval, design problems of variables and image denoising, digital fractional order for different filters [3,4,5,6,7,8,9]. The fractional calculus (differential operators) is used to reduce the error rate of handwritten signature verification system. All results based on the fractional calculus operators (differential and integral) show that this method is effective, and good immunity. The fractional calculus in the field of image processing and signal prosecuting that has broad application prospect
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