Accuracy, efficiency and optimization of signal fragmentation

Russel Caflisch, Hung Hsu Chou, Jonathan W. Siegel

Research output: Contribution to journalArticlepeer-review

Abstract

Signal fragmentation is the (approximate) representation of a signal as a sum of signal fragments, each of which has compact support. It has been proposed as a method for transmitting a low frequency signal over an array of small antennas. We present a mathematical analysis of signal fragmentation for an idealized model of antenna transmission. In the simplest form of signal fragmentation, each fragment has the same waveform, but the nth fragment has an amplitude an and is shifted in time by an amount tn = nΔ. We analyze the spectral leakage (i.e., the error in the Fourier representation) and energy efficiency of signal fragmentation. For a special choice of wavelet the spectral leakage can be eliminated for sinusoidal signals. We also formulate a measure of energy efficiency and perform a scaling analysis of the efficiency with a large number of fragments. Although the efficiency is poor for the original wavelet expansion, an alternative form of fragmentation has efficiency that scales well with the number of fragments. We then find the fragment waveform that optimizes the energy efficiency for a given choice of support size, and we generalize some of these results to AM signals.

Original languageEnglish (US)
Pages (from-to)737-757
Number of pages21
JournalMultiscale Modeling and Simulation
Volume18
Issue number2
DOIs
StatePublished - 2020

Keywords

  • Antenna transmission
  • Optimization
  • Signal fragmentation
  • Wavelets

ASJC Scopus subject areas

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications

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