Topology optimization of pulse shaping filters using the Hilbert transform envelope extraction

Authors:
Boyan Stefanov Lazarov;René Matzen;Yuriy Elesin
Affiliations:
Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, Lyngby, Denmark 2800;Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, Lyngby, Denmark 2800;Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, Lyngby, Denmark 2800
Venue:
Structural and Multidisciplinary Optimization
Year:
2011

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Abstract

Time domain topology optimization is applied to design pulse shaping filters. The objective function depends on the pulse envelope, which is extracted by utilizing the Hilbert transform. The gradients with respect to the topology optimization variables are derived, and the optimization methodology is demonstrated for pulse delaying and pulse splitting. The formulation is applicable for non-linear structures and signals consisting of broad range of frequencies.