calculateSpectrum: Function calculating and plotting the amplitude spectrum.
In baender/fats: Frequency Analysis of Time Series

Description Usage Arguments Details Value Author(s) Examples

The function calculates and plots the amplitude/energy spectrum via the FFT and also the corresponding frequencies or periods.

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calculateSpectrum(timeSignal, timeStep = 1, xAxis = "period",
  yAxis = "amplitude", xAxisLimits = c(0, 1), region = "half",
  plotFlag = TRUE)

`timeSignal`	Numeric vector; Time signal which should be transformed into the frequency domain.
`timeStep`	Numeric value (default: 1); Elapsed time between two data points.
`xAxis`	Character string (default: "period"); Either "frequency" or "period". Defining if on the x-axis the linear frequency or the reciprocal oscillation period is displayed.
`yAxis`	Character string (default: "amplitude"); Either "amplitude" or "energy". The spectral energy is proportional to the square of the amplitude. Normalized by the maximum energy.
`xAxisLimits`	Numeric vector of length 2 (default: c(0, 1)); Defines the range of the spectrum being displayed. 0 -> 0Hz/Inf Period, 1 -> Nyquist Frequency/Nyquist Period (twice the time step). The range is the same as for band edges during filter design in package signal (i.e. fir1())
`region`	Character string (default: "half"); Either "half" or "whole". Defines wether the region till the Nyquist frequency is shown or the range until the sample frequency with aliases.
`plotFlag`	Logical value (default: TRUE); Defining if amplitude/energy spectrum should be plotted or not.

This function takes a numeric vector containing the time series and returns the corresponding frequency spectrum over the full bandwidth 0Hz -> sample frequency.

Returns a list containing information about the time and frequency paratmeters, the original time series, the frequency spectrum and quantiles of the spectral energy.

Daniel Beiter, daniel.beiter@gfz-potsdam.de

N <- 200 # number of samples
d_t <- 2 # time step (temporal resolution)
A_1 <- 3 # signal amplitude
A_2 <- 5
A_3 <- 2
T_1 <- 5 # signal periods
T_2 <- 10
T_3 <- 25

t <- seq(from = 0, length.out = N, by = d_t) # setting up time vector
y <- A_1 * cos(2*pi / T_1 * t) +
     A_2 * cos(2*pi / T_2 * t) +
     A_3 * cos(2*pi / T_3 * t) # calculating signal values

frequencySpectrum <- calculateSpectrum(timeSignal = y, timeStep = d_t) # calculates the frequency spectrum