Waveform Relationships - A Deep Dive


Most test engineers are familiar with the FFT and PSD; these powerful mathematical tools allow them to analyze and understand the characteristics of a waveform, viewing energy and behaviors in the frequency domain that are hidden in a time domain view. Finding resonances and harmonics are common applications.

However, many engineers are not as familiar with the other math options that are used to understand the relationships between two or more waveforms. In complex products, frequency-dependent interactions can occur between the vibrations of multiple components and those interactions can move across all three axes. While they may be difficult to isolate, understanding these relationships is often key to recognizing how a test is affecting a product.

VR Software

Both VibrationVIEW and ObserVIEW offer users efficient access to sophisticated waveform relationship analysis using the transfer function, coherence, transmissibility, and cross-spectral density (VibrationVIEW also offers total harmonic distortion). In both software packages, a straightforward user interface makes it easy to apply these tools, view resulting graphs, and draw conclusions about the waveform interactions. To learn how the transfer function, coherence, cross-spectral density, and total harmonic distortion are implemented in VibrationVIEW, see the VRU course VibrationVIEW Analyzer Software Package. This course is designed to teach the basic concepts behind the tools and how to use them, not deliver an understanding of the underlying mathematics.

Coherence plot for aluminum mass vibrations in the X-axis (ch.3) and Y-axis (ch.4) compared to shaker head vibrations (vertical) (ch.1).


Some folks like to go deeper

Transfer function with measurement noise inputs

While a detailed background isn’t required, some engineers value the opportunity to delve into the mathematical foundation. For those customers, we have created a new VRU course, Mathematics for Understanding Waveform Relationships. This course provides a rigorous description of the math, which is, in fact, applicable to a broad range of technologies, not just vibration testing. Definitions, equations, proofs, and diagrams are all used in the explanations, then supplemented with example MATLAB® code and lists of references.

If this type of deep dive is not for you, take a look at our other VRU courses to see if there is something of interest. The courses are all free and we welcome your suggestions on future topics.



May 30, 2019


Thomas Roberts



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