phasegram: Phasegram

In soundgen: Sound Synthesis and Acoustic Analysis

Phasegram

Description

Produces a phasegram of a sound or another time series, which is a collection of Poincare sections cut through phase portraits of consecutive frames. The x axis is time, just as in a spectrogram, the y axis is a slice through the phase portrait, and the color shows the density of trajectories at each point of the phase portrait.

Usage

phasegram(
  x,
  samplingRate = NULL,
  from = NULL,
  to = NULL,
  windowLength = 10,
  step = windowLength/2,
  timeLag = NULL,
  theilerWindow = NULL,
  nonlinStats = c("ed", "d2", "ml", "sur"),
  pars_ed = list(max.embedding.dim = 15),
  pars_d2 = list(min.embedding.dim = 2, min.radius = 0.001, n.points.radius = 20),
  pars_ml = list(min.embedding.dim = 2, radius = 0.001),
  pars_sur = list(FUN = nonlinearTseries::timeAsymmetry, K = 1),
  bw = 0.01,
  bins = 5/bw,
  reportEvery = NULL,
  cores = 1,
  rasterize = FALSE,
  plot = TRUE,
  savePlots = NULL,
  colorTheme = c("bw", "seewave", "heat.colors", "...")[1],
  col = NULL,
  xlab = "Time",
  ylab = "",
  main = NULL,
  width = 900,
  height = 500,
  units = "px",
  res = NA,
  ...
)

Arguments

x	path to a folder, one or more wav or mp3 files c('file1.wav', 'file2.mp3'), Wave object, numeric vector, or a list of Wave objects or numeric vectors
samplingRate	sampling rate of x (only needed if x is a numeric vector)
from, to	if NULL (default), analyzes the whole sound, otherwise from...to (s)
windowLength	the length of each frame analyzed separately (ms)
step	time step between consecutive frames (ms)
timeLag	time lag between the original and time-shifted version of each frame that together represent the phase portrait (ms). Defaults to the number of steps beyond which the mutual information function reaches its minimum or, if that fails, the steps until mutual information experiences the first exponential decay - see timeLag
theilerWindow	time lag between two points that are considered locally independent and can be treated as neighbors in the reconstructed phase space. defaults to the first minimum or, if unavailable, the first zero of the autocorrelation function (or, failing that, to timeLag * 2)
nonlinStats	nonlinear statistics to report: "ed" = the optimal number of embedding dimensions, "d2" = correlation dimension D2, "ml" = maximum Lyapunov exponent, "sur" = the results of surrogate data testing for stochasticity. These are calculated using the functionality of the package nonlinearTseries, which is seriously slow, so the default is just to get the phasegram itself
pars_ed	a list of control parameters passed to estimateEmbeddingDim
pars_d2	a list of control parameters passed to corrDim
pars_ml	a list of control parameters passed to maxLyapunov
pars_sur	a list of control parameters passed to surrogateTest
bw	standard deviation of the smoothing kernel, as in density
bins	the number of bins along the Y axis after rasterizing (has no effect if rasterize = FALSE)
reportEvery	when processing multiple inputs, report estimated time left every ... iterations (NULL = default, NA = don't report)
cores	number of cores for parallel processing
rasterize	if FALSE, only plots and returns Poincare sections on the original scale (most graphical parameters will then have no effect); if TRUE, rasterizes the phasegram matrix and plots it with more graphical parameters
plot	should a spectrogram be plotted? TRUE / FALSE
savePlots	full path to the folder in which to save the plots (NULL = don't save, ” = same folder as audio)
colorTheme	black and white ('bw'), as in seewave package ('seewave'), matlab-type palette ('matlab'), or any palette from palette such as 'heat.colors', 'cm.colors', etc
col	actual colors, eg rev(rainbow(100)) - see ?hcl.colors for colors in base R (overrides colorTheme)
xlab, ylab, main	graphical parameters passed to soundgen:::filled.contour.mod (if rasterize = TRUE) or plot (if rasterize = FALSE)
width, height, units, res	graphical parameters for saving plots passed to png
...	other graphical parameters passed to soundgen:::filled.contour.mod (if rasterize = TRUE) or plot (if rasterize = FALSE)

Details

Algorithm: the input sound is normalized to [-1, 1] and divided into consecutive frames windowLength ms long without multiplying by any windowing function (unlike in STFT). For each frame, a phase portrait is obtained by time-shifting the frame by timeLag ms. A Poincare section is taken through the phase portrait (currently at a fixed angle, namely the default in poincareMap), giving the intersection points of trajectories with this bisecting line. The density of intersections is estimated with a smoothing kernel of bandwidth bw (as an alternative to using histogram bins). The density distributions per frame are stacked together into a phasegram (output: "orig"). The ranges of phase portraits depend on the amplitude of signal in each frame. The resulting phasegram can optionally be rasterized to smooth it for plotting (output: "rasterized").

Value

Returns a list of three components: "orig" = the full phasegram; "rasterized" = a rasterized version. For both, $time is the middle of each frame (ms), $x is the coordinate along a Poincare section (since the audio is normalized, the scale is [-1, 1]), and $y is the density of intersections of system trajectories with the Poincare section. The third component is $descriptives, which gives the result of nonlinear analysis per frame. Currently implemented: shannon = Shannon entropy of Poincare sections, nPeaks = log-number of peaks in the density distribution of Poincare sections, ml = maximum Lyapunov exponent (positive values suggest chaos), ed = optimal number of embedding dimensions (shows the complexity of the reconstructed attractor), d2 = correlation dimension, sur = probability of stochasticity according to surrogate data testing (0 = deterministic, 1 = stochastic).

References

• Herbst, C. T., Herzel, H., Švec, J. G., Wyman, M. T., & Fitch, W. T. (2013). Visualization of system dynamics using phasegrams. Journal of the Royal Society Interface, 10(85), 20130288.

• Huffaker, R., Huffaker, R. G., Bittelli, M., & Rosa, R. (2017). Nonlinear time series analysis with R. Oxford University Press.

Examples

target = soundgen(sylLen = 300, pitch = c(350, 420, 420, 410, 340) * 3,
  subDep = c(0, 0, 60, 50, 0, 0) / 2, addSilence = 0, plot = TRUE)
# Nonlinear statistics are also returned (slow - disable by setting
# nonlinStats = NULL if these are not needed)
ph = phasegram(target, 16000, nonlinStats = NULL)

## Not run: 
ph = phasegram(target, 16000, windowLength = 20, step = 20,
  rasterize = TRUE, bw = .01, bins = 150)
ph$descriptives

# Unfortunately, phasegrams are greatly affected by noise. Compare:
target2 = soundgen(sylLen = 300, pitch = c(350, 420, 420, 410, 340) * 3,
  subDep = c(0, 0, 60, 50, 0, 0)/2, noise = -10, addSilence = 0, plot = TRUE)
ph2 = phasegram(target2, 16000)

s2 = soundgen(sylLen = 3000, addSilence = 0, temperature = 1e-6,
  pitch = c(380, 550, 500, 220), subDep = c(0, 0, 40, 0, 0, 0, 0, 0),
  amDep = c(0, 0, 0, 0, 80, 0, 0, 0), amFreq = 80,
  jitterDep = c(0, 0, 0, 0, 0, 3))
spectrogram(s2, 16000, yScale = 'bark')
phasegram(s2, 16000, windowLength = 10, nonlinStats = NULL, bw = .001)
phasegram(s2, 16000, windowLength = 10, nonlinStats = NULL, bw = .02)

## End(Not run)

soundgen documentation built on Sept. 12, 2024, 6:29 a.m.