TY - JOUR
T1 - Unitary Equivalence
T2 - A New Twist on Signal Processing
AU - Baraniuk, Richard G.
AU - Jones, Douglas L.
N1 - Funding Information:
Manuscript received April 27, 1993; revised February 13, 1995. This work was completed while R. Baraniuk was with Ecole Normale Superieure de Lyon, France and was supported by an NSERC-NATO postdoctoral fellowship, the National Science Foundation, grant nos. ME’ 90-12747 and ME’ 94-57438, the Texas Advanced Technology Program, grant no. TX-ATP 003604-002, and the Joint Services Electronics Program, grant no. N00014-90-J-1270. The associate editor coordinating the review of this paper and approving it for publication was Dr. Boualem Boashash.
PY - 1995/12
Y1 - 1995/12
N2 - Unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time, frequency, and scale. Implementation of these new tools involves simply preprocessing the signal by a unitary transformation, performing standard processing on the transformed signal, and then (in some cases) transforming the resulting output. The resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and, hence, prove useful for representing and processing signals that are not well matched by current techniques. As specific examples of this procedure, we generalize linear time-invariant systems, orthonormal basis and frame decompositions, and joint time-frequency and time-scale distributions. These applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature.
AB - Unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time, frequency, and scale. Implementation of these new tools involves simply preprocessing the signal by a unitary transformation, performing standard processing on the transformed signal, and then (in some cases) transforming the resulting output. The resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and, hence, prove useful for representing and processing signals that are not well matched by current techniques. As specific examples of this procedure, we generalize linear time-invariant systems, orthonormal basis and frame decompositions, and joint time-frequency and time-scale distributions. These applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature.
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U2 - 10.1109/78.469861
DO - 10.1109/78.469861
M3 - Article
AN - SCOPUS:0029394521
SN - 1053-587X
VL - 43
SP - 2269
EP - 2282
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 10
ER -