A Compressed Sensing Approach to Signal Fragmentation
Abstract
This project is on a mathematical approach to signal fragmentation, as proposed by Dr. Richard Albanese, including mathematical formulation, analysis and optimization. The proposal of Albanese is for a method to send (relatively) long wavelength signals over an array of small antennas. Signal fragmentation approximates a desired signal f(t) (the input current to the antenna) by a sum of wavelets, each of which has the same shape phi(t), but with the n-th term shifted in time by an amount tn and scaled by a factor an. The wavelet phi is assumed to have compact support in time and successive wavelets are sent over different antennas, so that none of the fragments overlap in time. The objective of our project was to improve the design process, the accuracy, and the efficiency of signal fragmentation. Although we originally proposed to apply methods from compressed sensing and related fields, we found a better approach based on harmonic analysis, wavelets and approximation theory. With this approach, we succeeded in answering most of the questions that emerged from the research of Albanese, including development of a unified theory from antenna input to far field, analysis of spectral leakage for signal fragmentation, elimination of spectral leakage for sinusoidal signals, approximation of AM signals, energy efficiency of signal fragmentation, and optimal choice of wavelet.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 28, 2019
- Accession Number
- AD1086110
Entities
People
- Russel E. Caflisch
- Stanley Osher
Organizations
- University of California