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The main advantage of it is its high order differentiation capability.
The hidden periodicity can be revealed in the n-th order differentiation of the images.
Fractional calculus dates from 300 years ago and deals with arbitrary (noninteger) order differentiation and integration.
Fractional calculus was originated from a question of L'Hospital, in which he asked about the generalization of integral order differentiation.
As the SG filter is a nonlinear weighted smoothing function, it makes sure that high frequency noise amplified during second order differentiation is well suppressed.
Various processing methods such as polynomial fitting, first and second order differentiation, frequency domain filtering etc. have been used for this purpose.
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This paper presents a non-integer order differentiation-based FIR bandpass filter design method for ECG signals.
Similar to integer-order differentiation, Caputo fractional differential has the linear property: D^{alpha} bigl( c_{1}f_{1}(t)+c_{2}f_{2}(t) bigr) =c_{1}D^{alpha}f_{1}(t)+c_{2}D^{alpha}f_{2}(t), where (c_{1}) and (c_{2}) are constants.
Then, the filtered signal, f[n] (n denotes sampling points), is differentiated using five-point first-order differentiation to provide information about the slope of the QRS complexes and reduce the influence of the P and T waves [43].
The ACF and PACF for first-order differentiated data are shown in figure 3. The autocorrelations of the series after first-order differentiation is within 95% CI except for the first lag.
b A second-order differentiation map.
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