National Instruments Order Analysis Toolset - Manual (Page 25)

Chapter 2 Order Analysis
LabVIEW Order Analysis Toolset User Manual 2-10 ni.com
Currently, the following methods generally are used to perform order
analysis:
• Gabor transform
• Resampling
• Adaptive filter
The LabVIEW Order Analysis Toolset provides the
Gabor-transform-based method and the resampling method of order
analysis.
Gabor Transform
The Gabor transform is one of the invertible joint time-frequency
transforms. With invertible joint time-frequency transforms, you can
recover any time-domain input signal or an approximation of the signal by
applying an inverse transform to the transform of the signal. The Gabor
transform result is called a Gabor coefficient. The inverse Gabor transform
is known as the Gabor expansion. You can think of the Gabor transform as
a specific STFT. Even though you can recover a signal from its Gabor
transform by using a Gabor expansion, you cannot reconstruct the general
STFT using an inverse Fourier transform.
You can compute the Gabor transform by either STFT or windowed Fourier
transform. However, to ensure reconstruction of the signal, you have to
carefully manage the ratio of the analysis window to the window shift step
and the capture of information at signal edges. Use the following methods
to ensure reconstruction of the signal.
• Make sure that the ratio between the length of the analysis window and
the window shift step is greater than or equal to 1. The ratio between
the length of the analysis window and the window shift step determines
the time overlap. By default in the LabVIEW Order Analysis Toolset,
the ratio is set to 4. For example, if the window length is 2,048, the
window shift is 512.
• Move the analysis window in such way that no information is missed,
especially at the beginning and the end of the data samples. Zero
padding and wrap padding are two commonly used methods for
dealing with the edge data. Figure 2-7 illustrates zero padding and
wrap padding.