Bilinear time-frequency distributions, which provide simultaneous high resolution in both time and frequency domains, offer advantages for the analysis of vibration signals where the harmonic components and sidebands may be closely spaced. However, the Choi-Williams exponential distribution is found to be unsuitable, and aliasing produced by distributions of the Cohen class also causes problems. An aliasfree exponential time-frequency distribution is introduced, which combines features of distributions of the Cohen class and the generalized Wigner distribution. The new distribution is shown to be well suited to the analysis of signals with transient components.

1.
Choi
H. I.
, and
Williams
W. J.
,
1989
, “
Improved Time-Frequency Representation of Multicomponent Signals using Exponential Kernels
,”
IEEE Transactions on Acoustics Speech and Signal Processing
, Vol.
37
, No.
6
, pp.
862
871
.
2.
Chui, C. K., 1992, An Introduction to Wavelets Volume I: Wavelet Analysis and Its Applications, Academic Press Inc.
3.
Diethorn
E. J.
,
1994
, “
The Generalized Exponential Time-Frequency Distribution
,”
IEEE Transactions on Signal Processing
, Vol.
42
, No.
5
, pp.
1028
1037
.
4.
Hlawatsch
F.
, and
Urbanke
R. L.
,
1994
, “
Bilinear Time-Frequency Representations of Signals: the Shift-Scale Invariant Class
,”
IEEE Transactions on Signal Processing
, Vol.
42
, No.
2
, pp.
257
366
.
5.
Jeong
J.
, and
Williams
W. J.
,
1992
a, “
Kernel Design for Reduced Interference Distributions
,”
IEEE Transactions on Signal Processing
, Vol.
40
, No.
2
, pp.
402
412
.
6.
Jeong
J.
, and
Williams
W. J.
,
1992
b, “
Alias-Free Generalized Discrete-Time-Frequency Distributions
,”
IEEE Transactions on Signal Processing
, Vol.
40
, No.
11
, pp.
2757
2765
.
7.
Jones
D. L.
, and
Parks
T. W.
,
1992
, “
A Resolution Comparison of Several Time-Frequency Representations
,”
IEEE Transactions on Signal Processing
, Vol.
40
, No.
2
, pp.
412
420
.
8.
Martin
W.
, and
Flandrin
P.
,
1985
, “
Wigner-Ville Spectral Analysis of Nonstationary Processes
,”
IEEE Transactions on Acoustics Speech and Signal Processing
, Vol.
33
, No.
6
, pp.
1461
1470
.
9.
McFadden
P. D.
,
1987
, “
Examination of a Technique for the Early Detection of Failures in Gears by Signal Processing of the Time Domain Average of the Meshing Vibration
,”
Mechanical Systems and Signal Processing
, Vol.
1
, No.
2
, pp.
173
183
.
10.
McFadden
P. D.
,
1989
, “
Interpolation Techniques for Time Domain Averaging of Gear Vibration
,”
Mechanical Systems and Signal Processing
, Vol.
3
, No.
1
, pp.
87
97
.
11.
McFadden, P. D., and Zheng, G. T., 1993, “Application of the Wavelet Transform to the Early Detection of Gear Failure by Vibration Analysis,” Report OUEL 1999/93, Department of Engineering Science, University of Oxford.
12.
Stuckey, M. J., 1981, “Wessex Main Rotor Gearbox (MOD 1762) Fatigue Test—Vibration Monitoring—Trial No. 3 (final),” Mechanical Research Report MRR20-019, Westland Helicopters Ltd.
13.
Zhang
B.
, and
Sato
S.
,
1994
, “
A Time-Frequency Distribution of Cohens Class with a Compound Kernel and Its Application to Speech Signal Processing
,”
IEEE Transactions on Signal Processing
, Vol.
42
, No.
1
, pp.
54
64
.
14.
Zhao
Y. X.
,
Atlas
L. E.
, and
Marks
R. J.
,
1990
, “
The Use of Cone-Shaped Kernels for Generalized Time-Frequency Representations of Nonstationary Signals
,”
IEEE Transactions on Acoustics Speech and Signal Processing
, Vol.
38
, No.
7
, pp.
1084
1091
.
15.
Zheng, G. T., and McFadden, P. D., 1994, “Windowed Fourier Transform of Mechanical Vibration Signals,” Report OUEL 2036/94, Department of Engineering Science, University of Oxford.
This content is only available via PDF.
You do not currently have access to this content.