Fault Correlation Factor of Modes

Computes the fault correlation factor between a signal and each of its modes, a normalized inner product without removal of means.

Usage

measureFCF(signal, modes)

Arguments

signal: Finite numeric vector without dim.
modes: Finite numeric matrix with one row per sample of signal and one column per mode. Attributes other than dim do not reach the outputs.

Details

$$\mathrm{FCF}(x, c) = \frac{\sum_n x[n] c[n]}{\sqrt{\sum_n x[n]^2 \sum_n c[n]^2}}.$$ The means are not removed, so the factor differs from a correlation of centered vectors when the inputs have a nonzero mean.

Value

Numeric vector with one factor per mode.

Conditions

A signal or a mode of zero norm stops the function with an error of class xemdZeroEnergy.

Examples

Time <- seq_len(1000) / 1000
Tones <- cbind(cos(2 * pi * 2 * Time), 0.25 * cos(2 * pi * 24 * Time),
               0.0625 * cos(2 * pi * 288 * Time))
measureFCF(signal = rowSums(Tones), modes = Tones)
#> [1] 0.96836405 0.24209101 0.06052275