Fourier Cross Spectral Analysis Object and Template – Coherence (Spectral Analysis Option)

23.08.2021

The Coherence spectral procedure generates spectra that reflect the similarity across two distinct signals. The coherence plot visualizes at which frequencies two signals are coherent or have similar spectral energy, and where two signals differ. Likewise valuable is a frequency spectrum that reports the Signal to Noise Ratio as a function of frequency.

The Coherence is calculated using Fourier transforms. The data streams must be uniformly sampled (constant sample increment) and of the same length.

Spectrum Type

The procedure offers the four spectrum types Coherence, SNR - Signal to Noise Ratio, SNR - Signal to Noise Ratio dB and SNR - Signal to Noise Ratio normalized dB. The coherence plot will vary from 0 to 1. A coherence of 0 at a given frequency means there is no similarity between the signals at this frequency. A coherence value of 1 at a given frequency means the spectral content in the signals at this frequency are identical. The Signal to Noise Ratio can be expressed directly, in decibels, or in decibels normalized to zero at the largest peak. For the dB normalized type, the Signal to Noise Ratio will have a maximum at 0 dB, and the Y value of the associated peak may be slightly positive as a consequence of the bin interpolation.

Windows

FlexPro offers a variety of tapering windows to reduce the spectral leakage. The Window adjustment field is used to set the spectral width, and thus the dynamic range, of adjustable windows. This field will be disabled for fixed windows.

Parameters

The Best Exact N composite algorithm is used for the FFT.

The length of individual data segments, Segment Length and the amount of overlap, Overlap % can be specified. You should set the segment size based on the resolution needed. You can enter 0 for the segment length to set it to the data length / 4. Values for the overlap that produce the minimum variance are reported to be in the range of 50 to 70%.

To accommodate zero padding the FFT Length can be specified separately. Zero padding occurs when you set the FFT length to a value greater than the segment length. You can enter 0 for the FFT length to set it to the segment length. When a data tapering window is used, then zero-padding causes very little spectral leakage. Zero-padding is especially useful for interpolating peak frequencies with this algorithm, given the loss in resolution incurred by the reduced size of the segments.

Options - Peaks (Analysis Wizard Only)

The spectral peaks are identified by a local maxima detection algorithm. Both the spectral magnitude and the frequency locations of the detected peaks are based upon a cubic spline bin interpolation procedure.

The peaks can be set with a maximum peak count or a dB threshold below the largest peak. Peaks are ranked by interpolated amplitude. Note that a target signal component count may not be realized as fewer peaks than this target may be detected.

You can view the Y  and/or X values of the peaks in the spectrum by pressing Toggle Labels.

Options - Set/Clear Reference (Analysis Wizard Only)

This function lets you compare various spectral procedures and settings. You can view a copy of the currently displayed spectrum in the lower pane by pressing Set Reference. Next, you can adjust additional settings that affect the display in the upper pane. With Clear Reference, you can remove the copy and the time signals will appear again.

FPScript Functions Used

Coherence

See Also

Analysis Objects

Spectral Analysis Option

Fourier Cross Spectral Analysis Object

Cross Spectral Measurements

FFT Algorithms

Fourier Spectral Analysis

Data Tapering Windows

Cross Spectral Analysis Tutorial

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