Cross-spectral Analysis
Cross-spectral analysis
Cross-spectral analysis describes the relationship between two signals rather than analysing each signal independently.
It is useful when you want to determine:
•whether two signals contain related frequency components;
•how strongly they are related at each frequency;
•the phase difference between them;
•the relative level of one signal compared with another;
•the response of a system to a measured input;
•a time delay or similarity between two signals.
All two-signal analysis functions described on this page are available through Signal Calculator.
For meaningful results, the two signals should normally be measured or prepared using compatible sampling parameters and should represent synchronized data when the analysis requires a time or phase relationship.
Cross-correlation
Cross-correlation measures the similarity between two signals as one signal is shifted relative to the other.
It is commonly used for:
•detecting a time delay between signals;
•finding a known pattern in another signal;
•echo detection;
•comparing signals measured at different locations;
•identifying repeated or delayed responses.
The horizontal axis of the result represents relative shift between the signals.
SIGVIEW's cross-correlation result is not normalized to the range [-1, 1]. Therefore, the absolute amplitude of the result should not be interpreted as a normalized correlation coefficient.
SIGVIEW displays one half of the conventional two-sided cross-correlation result. The displayed side depends on the order of the source signals.
To inspect the opposite lag direction, reverse the signal order in Signal Calculator:
A Cross-correlation B
and:
B Cross-correlation A
Cross spectrum
The cross spectrum describes the frequency-domain relationship between two signals.
In general cross-spectral analysis, the cross spectrum is obtained from the complex spectra of the two signals and therefore contains both magnitude and phase information.
Frequency components that are present in a related way in both signals are emphasized, while unrelated components contribute less consistently, especially when spectral averaging is used.
Cross spectrum is often used as an intermediate quantity for calculations such as coherence and Frequency Response Functions.
Cross coherence
Cross coherence indicates how consistently two signals are linearly related at each frequency.
The result is normalized to the range:
0 ... 1
A value close to 1 indicates a strong and consistent relationship between the two signals at that frequency.
A value close to 0 indicates that little consistent linear relationship is present at that frequency.
Low coherence may be caused by noise, unrelated signal components, nonlinear behaviour, time variance, insufficient averaging, or a weak response at that frequency.
Coherence is particularly useful together with FRF measurements because it helps evaluate whether an FRF value is supported by a consistent input/output relationship.
Cross gain
Cross gain shows the frequency-dependent contribution of the first signal to the relationship between the two signals.
Because the result depends on signal order, the following two calculations are generally different:
Signal A Cross gain Signal B
Signal B Cross gain Signal A
When cross gain is important for your analysis, inspect both signal orders.
Phase shift
Phase shift displays the phase relationship between two signals as a function of frequency.
The result is shown in degrees, normally within: -180° ... +180°
The sign of the phase depends on the order of the source signals. Reversing the two inputs reverses the direction of the phase relationship.
Phase results are most meaningful at frequencies where both signals contain sufficient energy and have a stable relationship. Coherence can help identify frequencies where the measured phase relationship is reliable.
Relative spectrum (dBr)
Relative spectrum compares the spectral magnitude of two signals using a logarithmic ratio.
It is calculated as:
20 * log10(Spectrum1 / Spectrum2)
The result is expressed in dBr (decibels relative to the second signal).
Examples include:
•comparing a measured spectrum with a reference spectrum;
•evaluating gain or attenuation relative to a reference measurement;
•compensating for known microphone or sensor characteristics.
The order of the signals is important. Swapping Spectrum1 and Spectrum2 changes the sign of the result.
Frequency Response Function (FRF)
A Frequency Response Function describes the frequency-dependent relationship between an input signal and the corresponding output signal of a system.
SIGVIEW provides:
•FRF magnitude
•FRF phase
These functions are available in Signal Calculator.
FRF is commonly used for vibration analysis, modal testing, impact-hammer measurements, acoustics, and other input/output system measurements.
See Frequency Response Function (FRF) for a detailed description and usage recommendations.
Spectral-analysis settings
Cross-spectral calculations use SIGVIEW's spectral-analysis settings. Depending on the selected function, settings such as segmentation, averaging, windowing, and zero padding can affect the result.
The global defaults can be configured under:
Signal tools > Spectral analysis defaults
After a cross-spectral result has been created, its parameters can be changed through the result window's Properties dialog.
Averaging is especially important for noisy or stochastic two-channel measurements because it can improve the stability of cross-spectral, coherence, and FRF estimates.
See Spectral Analysis Defaults for details.