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   -> Volume 3, Issue 4


Announcement: Time-Frequency Distribution Series
 
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Shie Qian (qian@eagle.natinst.com)
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PostPosted: Mon Dec 02, 2002 12:50 pm    
Subject: Announcement: Time-Frequency Distribution Series
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Announcement: Time-Frequency Distribution Series

Time-Frequency Distribution Series

While widely recognized for its usefulness in time-varying
signal analysis, the Wigner-Ville distribution (WVD) has seldom
been used in real applications, mainly because of the so-called
cross-term interference. The traditional approach to lessen cross-
term interference has been to apply a weighting function (or kernel
function) in the ambiguity domain suppressing the terms away
from the origin. This process can be described as the linear
lowpass filtering. As an alternative, we suggest directly separating
the cross-term in the time-frequency domain. The procedure is
described as follows.
First, use the orthogonal-like Gabor expansion to decompose
the analyzed signal in terms of the linear combination of time and
the frequency-shifted single prototype Gaussian function. Then
take the WVD, with respect to the orthogonal-like Gabor
expansion, and obtain a linear combination of elementary WVD
(WVD of a pair of Gabor basis functions). Because the influence
of each individual elementary WVD on the useful properties is
inversely proportional to the distance between the corresponding
pair of Gabor basis functions, one can selectively remove the
elementary WVD, which is insignificant to the useful properties.
Unlike the traditional method mentioned earlier, this process is
equivalent to nonlinear 2D lowpass filtering.
Based on this contribution to the useful properties and the
degree of oscillation, we further group the elementary WVD and
represent the WVD in terms of group time-frequency functions,
named time-frequency distribution series (TFDS). The zero-order
TFDS is non-negative and is similar to the magnitude of the short-
time Fourier transform with using the Gaussian window function.
As the order increases, the resolution of the TFDS improves.
When the order approaches the infinite, the TFDS converges on the
WVD. By adjusting the order, one can balance the cross-term
interference and useful properties (such as marginal conditions and
resolution). The best compromise found is order three to four.
Over the past two years, the TFDS has been tested among
National Instruments applications in a variety of areas with
promising results, including:

* speech analysis (Northwest University Medical School)
* aneurysm research (Center for Clinical Neurophysiology,
University of Pittsburgh)
* non-destructive evaluation (University of Massachusetts at
Dartmouth)
* economic data analysis (Ilge Prigogine Center, University
of Texas at Austin)

The TFDS conference paper is posted in National Instruments
public folder.

login ftp.natinst.com
user anonymous
password (your email address)
cd support/labview/common_questions
get TFDS.ps

The TFDS software (part of the Joint Time-Frequency Analyzer
Toolkits) is also available. For more information, please contact
National Instruments, 6504 Bridge Point Parkway, Austin, Texas
78730-5039, (512) 794-0100. Or call toll free in the U.S. and
Canada at (800) 433-3488. Fax: (512) 794-8411.
All times are GMT + 1 Hour
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