TY - GEN
T1 - Enveloped Sinusoid Parseval Frames
AU - Goehle, Geoff
AU - Cowen, Benjamin
AU - Park, J. Daniel
AU - Brown, Daniel
N1 - Funding Information:
This work was sponsored in part by the Department of the Navy, Office of Naval Research under ONR award numbers N00014-18-1-2820 and N00014-19-1-2221.
Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - This paper presents a method of constructing Parseval frames from any collection of complex envelopes. The resulting Enveloped Sinusoid Parseval (ESP) frames can represent a wide variety of signal types as specified by their physical morphology. Since the ESP frame retains its Parseval property even when generated from a variety of envelopes, it is compatible with large scale and iterative optimization algorithms. The ESP construction provides an analysis and synthesis transform pair that can be tuned according to the characteristics of the signal to which it is applied. This work provides examples of ESP frame generation for both synthetic and experimentally measured signals. Furthermore, the frame's compatibility with distributed sparse optimization frameworks is demonstrated. Numerical experiments on acoustics data reveal that the flexibility of this method allows it to be simultaneously competitive with a signal agnostic short-time Fourier Transform in time-frequency processing and also with Prony's Method for time-constant parameter estimation, surpassing the shortcomings of each individual technique.
AB - This paper presents a method of constructing Parseval frames from any collection of complex envelopes. The resulting Enveloped Sinusoid Parseval (ESP) frames can represent a wide variety of signal types as specified by their physical morphology. Since the ESP frame retains its Parseval property even when generated from a variety of envelopes, it is compatible with large scale and iterative optimization algorithms. The ESP construction provides an analysis and synthesis transform pair that can be tuned according to the characteristics of the signal to which it is applied. This work provides examples of ESP frame generation for both synthetic and experimentally measured signals. Furthermore, the frame's compatibility with distributed sparse optimization frameworks is demonstrated. Numerical experiments on acoustics data reveal that the flexibility of this method allows it to be simultaneously competitive with a signal agnostic short-time Fourier Transform in time-frequency processing and also with Prony's Method for time-constant parameter estimation, surpassing the shortcomings of each individual technique.
UR - http://www.scopus.com/inward/record.url?scp=85145768704&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85145768704&partnerID=8YFLogxK
U2 - 10.1109/OCEANS47191.2022.9977041
DO - 10.1109/OCEANS47191.2022.9977041
M3 - Conference contribution
AN - SCOPUS:85145768704
T3 - Oceans Conference Record (IEEE)
BT - OCEANS 2022 Hampton Roads
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 OCEANS Hampton Roads, OCEANS 2022
Y2 - 17 October 2022 through 20 October 2022
ER -