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A wavelet-based measurement of signal fractal dimensions
Langi A.Z.R.a, Nugraha H.B.a
a DSP Research and Technology Group, Department of Electrical Engineering, Bandung Institute of Technology, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]This paper describes a study of measuring signal fractal dimensions (especially in a form of Lipschitz exponents γ) using wavelets. The procedure is as follows. Given a one-dimensional signal f(t) and its corresponding wavelet transform (at a scale a and a position b) as Wf (a, b), we find wavelet maxima lines l(a,b) and their corresponding wavelet maxima |Wf(a,b)|. Suppose the signal f(t) has a Lipschitz exponent γ at t = b0, and there is a maxima line l(a,b) reaching b0 as a→0. The corresponding wavelet maxima in the line satisfy an inequality |Wf(a,b)|≤Caγ+0.5 for some constant C and a→0. A log-log plot on the inequality estimates the Lipschitz exponent γ. We have performed an experiment of the procedure for f(t)=1-|0.5-t|γ, where the Lipschitz component γ varies from 0.1 to 0.9 at a 0.1 interval. The procedure provides relatively good estimates for 0.5 ≤ γ ≤ 0.9, with relative errors less than 10%.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Signal fractal dimensions[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Fractal dimension,Lipschitz exponent,Modulus maxima,Wavelet transform[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]