tfestimate function

Transfer Function Estimate

Finds a transfer function estimate for signals.

tfestimate(
  x,
  window = nextpow2(sqrt(NROW(x))),
  overlap = 0.5,
  nfft = ifelse(isScalar(window), window, length(window)),
  fs = 1,
  detrend = c("long-mean", "short-mean", "long-linear", "short-linear", "none")
)

tfe(
  x,
  window = nextpow2(sqrt(NROW(x))),
  overlap = 0.5,
  nfft = ifelse(isScalar(window), window, length(window)),
  fs = 1,
  detrend = c("long-mean", "short-mean", "long-linear", "short-linear", "none")
)

Arguments

• x: input data, specified as a numeric vector or matrix. In case of a vector it represents a single signal; in case of a matrix each column is a signal.

• window: If window is a vector, each segment has the same length as window and is multiplied by window before (optional) zero-padding and calculation of its periodogram. If window is a scalar, each segment has a length of window and a Hamming window is used. Default: nextpow2(sqrt(length(x))) (the square root of the length of x rounded up to the next power of two). The window length must be larger than 3.

• overlap: segment overlap, specified as a numeric value expressed as a multiple of window or segment length. 0 <= overlap < 1. Default: 0.5.

• nfft: Length of FFT, specified as an integer scalar. The default is the length of the window vector or has the same value as the scalar window argument. If nfft is larger than the segment length, (seg_len), the data segment is padded nfft - seg_len zeros. The default is no padding. Nfft values smaller than the length of the data segment (or window) are ignored. Note that the use of padding to increase the frequency resolution of the spectral estimate is controversial.

• fs: sampling frequency (Hertz), specified as a positive scalar. Default: 1.

• detrend: character string specifying detrending option; one of:

  • "long-mean": remove the mean from the data before splitting into segments (default)
  • "short-mean": remove the mean value of each segment
  • "long-linear": remove linear trend from the data before splitting into segments
  • "short-linear": remove linear trend from each segment
  • "none": no detrending

Returns

A list containing the following elements:

• freq: vector of frequencies at which the spectral variables are estimated. If x is numeric, power from negative frequencies is added to the positive side of the spectrum, but not at zero or Nyquist (fs/2) frequencies. This keeps power equal in time and spectral domains. If x is complex, then the whole frequency range is returned.
• trans: NULL for univariate series. For multivariate series, a matrix containing the transfer function estimates between different series. Column $i + (j - 1) * (j - 2)/2$ of coh contains the cross-spectral estimates between columns $i$ and $j$ of $x$, where $i < j$.

Details

tfestimate uses Welch's averaged periodogram method.

Note

The function tfestimate (and its deprecated alias tfe) is a wrapper for the function pwelch, which is more complete and more flexible.

Examples

fs <- 1000
f <- 250
t <- seq(0, 1 - 1/fs, 1/fs)
s1 <- sin(2 * pi * f * t) + runif(length(t))
s2 <- sin(2 * pi * f * t - pi / 3) + runif(length(t))
rv <- tfestimate(cbind(s1, s2), fs = fs)
plot(rv$freq, 10*log10(abs(rv$trans)), type="l", xlab = "Frequency",
 ylab = "Tranfer Function Estimate (dB)", main = colnames((rv$trans)))

h <- fir1(30, 0.2, window = rectwin(31))
x <- rnorm(16384)
y <- filter(h, x)
tfe <- tfestimate(cbind(x, y), 1024, fs = 500)
plot(tfe$freq, 10*log10(abs(tfe$trans)), type="l", xlab = "Frequency",
  ylab = "Tranfer Function Estimate (dB)", main = colnames((tfe$trans)))

See Also

pwelch

Author(s)

Peter V. Lanspeary, pvl@mecheng.adelaide.edu.au .

Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com .