TY - GEN
T1 - Lower and upper bounds for the error of the Jth resolution via optimal wavelet choice for a signal
AU - Xia, X. G.
AU - Zhang, Z.
N1 - Publisher Copyright:
© 1992 IEEE.
PY - 1992
Y1 - 1992
N2 - In this article, we investigate how to select a wavelet for a given signal such that the error of the discrete wavelet representation up to a given scale is minimized. We derive lower and upper bounds for the error of the Jth resolution fj of f with respect to f itself when the Fourier spectrum off is mostly concentrated in [-2J π, 2J7 π] .T he lower and the upper bounds we derive are only different from each other by a positive constant multiple. Based on the error bounds, the cost function is choosen as the upper bound with quadratic form of unknown coefficients. Then the optimal coefficients of the Daubechies wavelets are formulated as solutions of some quadratic equations, which depend on the signal and J. We also consider optimal wavelets in signal independent case. 1992 IEEE.
AB - In this article, we investigate how to select a wavelet for a given signal such that the error of the discrete wavelet representation up to a given scale is minimized. We derive lower and upper bounds for the error of the Jth resolution fj of f with respect to f itself when the Fourier spectrum off is mostly concentrated in [-2J π, 2J7 π] .T he lower and the upper bounds we derive are only different from each other by a positive constant multiple. Based on the error bounds, the cost function is choosen as the upper bound with quadratic form of unknown coefficients. Then the optimal coefficients of the Daubechies wavelets are formulated as solutions of some quadratic equations, which depend on the signal and J. We also consider optimal wavelets in signal independent case. 1992 IEEE.
UR - http://www.scopus.com/inward/record.url?scp=85068707901&partnerID=8YFLogxK
U2 - 10.1109/TFTSA.1992.274172
DO - 10.1109/TFTSA.1992.274172
M3 - Conference contribution
AN - SCOPUS:85068707901
T3 - Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
SP - 327
EP - 330
BT - Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
Y2 - 4 October 1992 through 6 October 1992
ER -