National Instruments Order Analysis Toolset

Appendix A Gabor Expansion and GaborTransform

4. Compute the new Gabor coefficients after you obtain the time

waveform.

5. Repeat steps 1 through 4 until the time waveforms converge.

Without a loss of generality, rewrite the Gabor expansion from

Equation A-1 and the Gabor transform from Equation A-2 in matrix form,

as shown in the following equations.

where H denotes the analysis matrix and G denotes the synthesis matrix.

Notice that for over sampling, the following relationships are true.

Therefore, in the case of over sampling, the iterative process is described

by the following equations.

CGs=

TGs=

HTGI=GHTI≠

ˆ1ΦC=

s1HTC

ˆ1

C2Gs1GHTΦC==

ˆ2ΦC2

s2HTC

ˆ2

C3Gs2GHTΦGHTΦCGH

TΦ()

2C== =

…

CkGHTΦ()

k1–C=

Contents

Main Page Important Information Warranty Copyright Trademarks Patents Contents About This Manual Chapter 1 Introduction to the LabVIEW Order Analysis Toolset Chapter 2 Order Analysis Page About This Manual How to Use This Manual Conventions Related Documentation Introduction to the LabVIEW Order Analysis Toolset Overview of the LabVIEW Order Analysis Toolset Overview of the LabVIEW Order Analysis Start-Up Kit Important Considerations for the Analysis of Rotating Machinery System Requirements Installation Example VIs Acquiring Data for Example VIs Configuring DAQ Hardware Used with Examples Acquire Data (Analog Tach) VI Acquire Data with PXI 4472 and TIO VI Page Page Order Analysis Order Analysis Definition and Application Order Analysis Basics Page Page Effect of Rotational Speed on Order Identification Constant Rotational Speed Page Variable Rotational Speed Page Page Harmonic Analysis Order Analysis Order Analysis Methods Gabor Transform Page Page Resampling Page Adaptive Filter Gabor Transform-Based Order Tracking Overview of Gabor Order Analysis Page Extracting the Order Components Page Masking Extracting Orders Reconstructing the Signal Displaying Spectral Maps Page Calculating Waveform Magnitude Resampling-Based Order Analysis LabVIEW Order Analysis Toolset Resampling Method Determining the Time Instance for Resampling Page Resampling Vibration Data Slow Roll Compensation Page Calculating Rotational Speed Digital Differentiator Method Page Averaging Pulses Page A Gabor Expansion and Gabor Transform Gabor Expansion and Gabor Transform Basics Page Page Discrete Gabor-Expansion-Based Time-Varying Filter Page Page B References C Technical Support and Professional Services Glossary Numbers/Symbols A C D Page R S W Index A C D E K M N O P