## Cross-spectral analysis

Cross-spectral analysis gives you information about relation between two signals in their frequency domain. All cross analysis functions are accessible through the Signal calculator.

The following functions are available:

Cross-correlation: The measure of similarity of two signals, commonly used to find features in an unknown signal by comparing it to a known one. It is a function of the relative time offset between the signals. It can also be used to detect similarities in possibly time-delayed signals in applications such as echo detection etc. Please note that amplitude values of the cross-correlation result are not fully normalised, i.e. maximal correlation will not have a value of 1. The result of the cross correlation function will only show one half of the common cross correlation plot (positive or negative, depending on the order of signals used in expression). To see the other side, simply switch the order of the signals used in your expression ("B cross corr. A" instead of "A cross corr. B").

Cross spectrum: The product of spectra of two signals. Similarities in their frequency domains will be emphasised.

Cross coherence: The measure of correspondence between spectra of two signals. The Y-axis units are normalised to [0,1]. The value of 1 means that this frequency component is very similar in both signals, the 0 means that there is no similarity.

Cross gain: The measure of the contribution of the signal1 frequency component in the cross spectrum of signal1 and signal2. Higher amplitude means that the first signal contributes more in the cross spectrum for that specific frequency. To take a full advantage of this analysis you should perform both “signal1 cross gain signal2” and “signal2 cross gain signal1” analysis.

Phase shift: The phase shift between signal1 and signal2 on different frequencies. The Y-axis amplitude is normalised to [-180,180] degrees.

Relative spectrum (dBr): The relative spectrum relation between two signals, calculated as 20*log (spectrum1/spectrum2). By using this function you can calculate the spectrum of the signal relative to some reference signal, for example, microphone input relative to microphone characteristics spectrum.

Frequency Response Function (FRF): Also sometimes referred as a “transfer function” between the input and output. Expresses the frequency domain relationship between the input (x) and output (y). It is a complex function, so SIGVIEW allows for the calculation of its FRF magnitude and FRF phase. FRF magnitude is calculated as crossspectrum( input, output ) / autospectrum( input ). FRF phase is the simply calculated as a phase shift between input and output signals. FRF magnitude calculation uses Exponential window as its default windowing function (can be changed in the properties of a result window).