tf: Estimate the frequency-domain transfer function
In driegert/transfer: Frequency Domain Transfer Function Estimation Tools

Description Usage Arguments Details Value

Estimates a transfer function between the columns of input x and the response y.

tf(x, y, blockSize = dim(x)[1], overlap = 0, deltat = 1, nw = 4,
  k = 7, nFFT = NULL, method = c("svd", "sft", "robust", "svdBendat"),
  lOrd = NULL, adaptiveWeighting = TRUE, interactionOrder = 0,
  freqRange = NULL, maxFreqOffset = NULL, cohSigCutoff = 0.9,
  useZeroOffset = TRUE, nOffsetFreq = -1, standardize = TRUE,
  prewhiten = TRUE, removePeriodic = TRUE, asMatrix = TRUE)

`x`	A `data.frame` whose columns are the time domain input series.
`y`	A single column `data.frame` containing the response series.
`blockSize`	A `numeric` indicating the block sizes into which the input and response series will be partitioned.
`overlap`	A `numeric` between 0 and 1 indicating how much overlap should exist between adjacent blocks.
`deltat`	A `numeric` indicating the sample rate.
`nw`	A `numeric` indicating the time bandwidth parameter for estimating the Slepian data tapers.
`k`	A `numeric` indicating the number of tapers to use - should be approximately floor(2nw - 1) and no larger than floor(2nw).
`nFFT`	A `numeric` indicating the number of frequency bins to use (i.e. setting the zeropadding amount).
`method`	A `character` string indicating which method to use. See details.
`lOrd`	A vector with length == numColumns of x. The order of the regression for svdBendat method.
`adaptiveWeighting`	A `logical` indicating whether the eigencoefficients should be multiplied by their adaptive weights before performing the regression. Note: Only implemented for `method = "svd"`.
`interactionOrder`	An `integer` indicating what order of interactions of the covariates to include in the linear regression model. A value of 0 would include the main effects only and no interactions. NOTE: there is currently no method to choose particulare interactions - all or none.
`freqRange`	A vector of length 2 containing the endpoints of the frequency range over which to calculate the offset coherences (these are central frequencies of the response).
`maxFreqOffset`	A `numeric` value in Hz indicating the largest offset to be calculated in both the positive and negative direction.
`useZeroOffset`	A `logical` value indicating whether to always in include the center frequency when taking offset frequencies into account.
`nOffsetFreq`	An `integer` indicating how many offset frequencies should be used (a maximum amount).
`standardize`	Should the inputs and outputs be standardized to have mean = 0 and standard deviation = 1?
`prewhiten`	NOT CURRENTLY IMPLEMENTED.
`removePeriodic`	NOT CURRENTLY IMPLEMENTED.
`asMatrix`	A `logical` which is only used during offset coherences - currently used in testing.

Takes the times series inputs and response, divides these series into (optionally) overlapping blocks, tapers each block with Discrete Prolate Spheriodal Sequences (DPSS's or Slepian sequences), Fourier transforms each block, uses the adaptive weights (method = "svd") and then estimates the transfer function at each frequency between the Fourier transforms of the inputs and the response.

The method argument indicates how the transfer function should be estimated. method = "sft" does the following; 1) a slow Fourier transform is used, 2) no adaptive weights are used and 3) the matrix definition of the regression coefficients are used: $(X^tX)^-1)X^-1y$ method = "svd" uses 1) the FFT, 2) adaptive weights, and 3) a singular value decomposition method for estimating the regression coefficients. method = "svdBendat" decorrelates the inputs prior to estimating the transfer functions, then obtains the appropriate transfer function after (see Chapter 7.3 of Bendat & Piersol). Overall - method = "svdBendat" is in all probability the better method to use.

An object of class transfer, consisting of a complex matrix whose columns are the individual transfer function for each input, and several attributes describing the transfer function estimate.

driegert/transfer documentation built on May 15, 2019, 2:11 p.m.