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Signal Waveform Comparison Resources


Signal waveform comparison can provide valuable insights during vibration testing. In complex environments, frequency-dependent interactions may occur between the vibrations of multiple components. These interactions are sometimes difficult to isolate but understanding them can help to identify a test’s impact on the device under test (DUT) or troubleshoot a test error.

Most vibration test engineers are familiar with the fast Fourier transform and power spectral density, which are powerful mathematical tools for waveform analysis. They may not be as familiar with the mathematics that helps explain the relationships between two or more waveforms. These interactions can move across the three linear axes and may be influenced by external factors such as noise.

Vibration Research University—a free online resource—includes two courses on signal waveform comparison. The first presents three software graph capabilities that help test engineers examine waveform relationships. The second provides a mathematical foundation for these comparison methods.

Software Graph Capabilities

The VibrationVIEW Analyzer software package helps engineers better understand complex relationships between signals. The software add-on enhances Sine, Random, and Shock tests by comparing the frequency content of two signals. The advanced graph options include transfer function, coherence, transmissibility, and cross-spectral density and help identify similarities and influences between waveforms.

The VibrationVIEW Analyzer Software Package course teaches the basic concepts behind these graphing tools and how to use them.

Coherence plot for aluminum mass vibrations in the X-axis and Y-axis compared to shaker head vibrations

Coherence plot in VibrationVIEW.

Mathematics of Waveform Relationships

Transfer function with measurement noise inputs

Transfer function with measurement noise inputs.

Some may also value the opportunity to delve into the mathematical foundations of waveform relationships. The Mathematics for Understanding Waveform Relationships course provides a rigorous description of the mathematics behind several methods of signal waveform comparison, and it applies to a broad range of technologies, not just vibration testing.

The course uses definitions, equations, proofs, and diagrams and is supplemented with example MATLAB® codes and reference lists.

More Resources


May 30, 2019


Thomas Roberts



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