This paper presents a fast adaptive time–frequency analysis method for dealing with the signals consisting of stationary components and transients, which are encountered very often in practice. It is developed based on the short-time Fourier transform but the window bandwidth varies along frequency adaptively. The method therefore behaves more like an adaptive continuous wavelet transform. We use B-splines as the window functions, which have near optimal time–frequency localization, and derive a fast algorithm for adaptive time–frequency representation. The method is applied to the analysis of vibration signals collected from rotating machines with incipient localized defects. The results show that it performs obviously better than the short-time Fourier transform, continuous wavelet transform, and several other most studied time–frequency analysis techniques for the given task.

1.
Lin
,
S. T.
, and
McFadden
,
P. D.
, 1997, “
Gear Vibration Analysis by B-Spline Wavelet-Based Linear Wavelet Transform
,”
Mech. Syst. Signal Process.
0888-3270,
11
, pp.
603
609
.
2.
Zheng
,
G. T.
, and
McFadden
,
P. D.
, 1999, “
Time-Frequency Distribution for Analysis of Signals with Transient Components and Its Application to Vibration Analysis
,”
ASME J. Vibr. Acoust.
0739-3717,
121
, pp.
328
333
.
3.
Boulahbal
,
D.
,
Golnaraghi
,
M. F.
, and
Ismail
,
F.
, 1999, “
Amplitude and Phase Wavelet Maps for the Detection of Cracks in Geared Systems
,”
Mech. Syst. Signal Process.
0888-3270,
13
, pp.
423
436
.
4.
Tse
,
P. W.
,
Peng
,
Y. H.
, and
Yam
,
R.
, 2001, “
Wavelet Analysis and Envelope Detection for Rolling Element Bearing Fault Diagnosis—Their Effectiveness and Flexibilities
,”
ASME J. Vibr. Acoust.
0739-3717,
123
, pp.
303
310
.
5.
Choy
,
F. K.
,
Mugler
,
D. H.
, and
Zhou
,
J.
, 2003, “
Damage Identification of a Gear Transmission Using Vibration Signatures
,”
J. Mech. Des.
1050-0472,
125
, pp.
394
403
.
6.
Lin
,
J.
,
Zuo
,
M. J.
, and
Fyfe
,
K. R.
, 2004, “
Mechanical Fault Detection Based on the Wavelet Denoising Technique
,”
ASME J. Vibr. Acoust.
0739-3717,
126
, pp.
9
16
.
7.
Cohen
,
L.
, 1995,
Time-Frequency Analysis
,
Prentice–Hall
,
Englewood Cliffs, NJ
.
8.
Jones
,
D. L.
, and
Parks
,
T. W.
, 1990, “
A High Resolution Data-Adaptive Time-Frequency Representation
,”
IEEE Trans. Acoust., Speech, Signal Process.
0096-3518,
38
, pp.
2127
2135
.
9.
Mallat
,
S. G.
, and
Zhang
,
Z.
, 1993, “
Matching Pursuits with Time-Frequency Dictionaries
,”
IEEE Trans. Signal Process.
1053-587X,
41
, pp.
3397
3415
.
10.
Huang
,
N. E.
,
Shen
,
Z.
,
Long
,
S. R.
,
Wu
,
N. 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. London, Ser. A
1364-5021,
454
, pp.
903
995
.
11.
Jones
,
D. L.
, and
Baraniuk
,
R. G.
, 1994, “
A Simple Scheme for Adapting Time-Frequency Representations
,”
IEEE Trans. Signal Process.
1053-587X,
42
, pp.
3530
3535
.
12.
deBoor
,
C.
, 1978,
A Practical Guide to Splines
,
Prentice–Hall
,
Englewood Cliffs, NJ
.
13.
Unser
,
M.
, 1999, “
Splines, A Perfect Fit for Signal and Image Processing
,” IEEE Signal Processing Magzine, November, pp.
22
38
.
14.
Unser
,
M.
,
Aldrobi
,
A.
, and
Eden
,
M.
, 1992, “
On the Asymptotic Convergence of B-Spline Wavelets to Gabor Functions
,”
IEEE Trans. Inf. Theory
0018-9448,
38
, pp.
864
872
.
15.
Nawab
,
S. H.
, and
Quatieri
,
T. F.
, 1988, “
Short-Time Fourier Transform
,”
Advanced Topics in Signal Processing
,
J. S.
Lim
and
A. V.
Oppenheim
, eds.,
Prentice–Hall
,
Englewood Cliffs, NJ
, pp.
289
337
.
16.
Braun
,
S.
, 1986,
Mechanical Signature Analysis
,
Academic
,
London
.
You do not currently have access to this content.