It is difficult to generate high-definition time-frequency maps for rapidly changing transient signals. New details of the theory of harmonic wavelet analysis are described which provide the basis for computational algorithms designed to improve map definition. Features of these algorithms include the use of ridge identification and phase gradient as diagnostic features.

1.
Brown
J. C.
,
1991
, “
Calculation of a Constant Q Spectral Transform
,”
J. Acoust. Soc. Am.
, Vol.
89
, No.
1
, pp.
425
434
.
2.
Brown
J. C.
, and
Puckette
M. S.
,
1992
, “
An Efficient Algorithm for the Calculation of a Constant Q Transform
,”
J. Acoust. Soc. Am.
, Vol.
92
, pp.
2698
2701
.
3.
Cohen, L., 1995, Time-Frequency Analysis, Prentice Hall, New Jersey.
4.
Eberly, D., 1996, Ridges in Image and Data Analysis, Kluwer, Boston, MA.
5.
Huang
N. E.
,
Shen
Z.
,
Long
S. R.
,
Wu
M. C.
,
Shih
H. H.
,
Zheng
Q.
,
Yen
N-C.
,
Tung
C. C.
and
Liu
H. H.
,
1998
, “
The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time-Series Analysis
,”
Proc. R. Soc. Lond. A
, Vol.
454
, pp.
903
995
.
6.
Koenderink
Jan J.
and
van Dorn
Andrea J.
,
1993
, “
Local Features of Smooth Shapes: Ridges and Courses
,”
Geometric Methods in Computer Vision, II, Proc. SPIE
, Vol.
2031
, pp.
2
13
.
7.
Newland
D. E.
,
1993
a, “
Harmonic Wavelet Analysis
,”
Proc. R. Soc. Lond. A
, Vol.
443
, pp.
203
225
.
8.
Newland, D. E., 1993b, Random Vibrations, Spectral and Wavelet Analysis, 3rd edition, Addison Wesley Longman.
9.
Newland
D. E.
,
1994
a, “
Harmonic and Musical Wavelets
,”
Proc. R. Soc. Lond. A
, Vol.
444
, pp.
605
620
.
10.
Newland
D. E.
,
1994
b, “
Wavelet Analysis of Vibration, Part 1: Theory
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
116
, pp.
409
416
.
11.
Newland
D. E.
,
1994
c, “
Wavelet Analysis of Vibration, Part 2: Wavelet Maps
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
116
, pp.
417
425
.
12.
Newland, D. E., 1997, “Practical Signal Analysis: Do Wavelets Make Any Difference?” Keynote Paper, Proc. 1997 ASME Design Engineering Technical Conferences, 16th Biennial Conf. on Mechanical Vibration and Noise, Paper DETC97/VIB-4135 (CD ROM ISBN 0 7918 1243 X), Sacramento, California.
13.
Newland, D. E., 1998, “Time-Frequency and Time-Scale Signal Analysis by Harmonic Wavelets,” Chapter 1, Signal Analysis and Prediction, A. Procha´zka, J. Uhli´r, P. J. W. Rayner and N. G. Kingsbury, eds., Birkha¨user, Boston.
14.
Skudrzyk, E., 1971, The Foundations of Acoustics, Springer-Verlag, Wien New York.
15.
Tchamitchian, Ph., and Torresani, B., 1992, “Ridge and Skeleton Extraction from the Wavelet Transform,” Chapter in Wavelets and Their Application, M. B. Ruskai, ed., Jones and Bartlett, Boston, MA, pp. 123–151.
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