A Robust Algorithm for Optimisation and Customisation of Fractal Dimensions of Time Series Modified by Nonlinearly Scaling Their Time Derivatives: Mathematical Theory and Practical Applications
Figure 4
Frequency reduction of a signal; (a) original signal at Hz; (b) signal reduced to Hz with two solutions (insert): every other even point (red) and every other odd point (green); insert: 2nd half of that green segment which precedes the first green line connecting points 2 and 4; (c) signal reduced to Hz with four solutions; (d) magnified part of Figure 4(c); the signal starts at 14.5 s; red, yellow, green, and blue lines start at points 1, 2, 3, and 4, respectively; therefore, , , and of the preceding yellow, green, and blue segments, respectively, have to be included such that each coloured signal starts at 14.5 s exactly.
