gsignal (version 0.3-1)

ar_psd: Power spectrum of AR model

Description

Compute the power spectral density of an autoregressive model.

Usage

ar_psd(
  a,
  v = 1,
  freq = 256,
  fs = 1,
  range = ifelse(is.numeric(a), "half", "whole"),
  method = ifelse(length(freq) == 1 && bitwAnd(freq, freq - 1) == 0, "fft", "poly")
)
# S3 method for ar_psd
plot(
  x,
  yscale = c("linear", "log", "dB"),
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  ...
)

Arguments

a

numeric vector of autoregressive model coefficients. The first element is the zero-lag coefficient, which always has a value of 1.

v

square of the moving average coefficient, specified as a positive scalar Default: 1

freq

vector of frequencies at which power spectral density is calculated, or a scalar indicating the number of uniformly distributed frequency values at which spectral density is calculated. Default: 256.

fs

sampling frequency (Hz). Default: 1

range

character string. one of:

"half" or "onesided"

frequency range of the spectrum is from zero up to but not including fs / 2. Power from negative frequencies is added to the positive side of the spectrum.

"whole" or "twosided"

frequency range of the spectrum is -fs / 2 to fs / 2, with negative frequencies stored in "wrap around order" after the positive frequencies; e.g. frequencies for a 10-point "twosided" spectrum are 0 0.1 0.2 0.3 0.4 0.5 -0.4 -0.3 -0.2. -0.1.

"shift" or "centerdc"

same as "whole" but with the first half of the spectrum swapped with second half to put the zero-frequency value in the middle. If freq is a vector, "shift" is ignored.

Default: If model coefficients a are real, the default range is "half", otherwise the default range is "whole".

method

method used to calculate the power spectral density, either "fft" (use the Fast Fourier Transform) or "poly" (calculate the power spectrum as a polynomial). This argument is ignored if the freq argument is a vector. The default is "poly" unless the freq argument is an integer power of 2.

x

object to plot.

yscale

character string specifying scaling of Y-axis; one of "linear", "log", "dB"

xlab, ylab, main

labels passed to plotting function. Default: NULL

...

additional arguments passed to functions

Value

An object of class "ar_psd" , which is a list containing two elements, freq and psd containing the frequency values and the estimates of power-spectral density, respectively.

Details

This function calculates the power spectrum of the autoregressive model

                       M
x(n) = sqrt(v).e(n) + SUM a(k).x(n-k)
                      k=1

where x(n) is the output of the model and e(n) is white noise.

Examples

# NOT RUN {
a <- c(1, -2.7607, 3.8106, -2.6535, 0.9238)
psd <- ar_psd(a)

# }