findpeaks {gsignal}

Find local extrema

Description

Return peak values and their locations of the vector data.

Usage

findpeaks(
  data,
  MinPeakHeight = .Machine$double.eps,
  MinPeakDistance = 1,
  MinPeakWidth = 1,
  MaxPeakWidth = Inf,
  DoubleSided = FALSE
)

Arguments

data

the data, expected to be a vector or one-dimensional array.

MinPeakHeight

Minimum peak height (non-negative scalar). Only peaks that exceed this value will be returned. For data taking positive and negative values use the option DoubleSided. Default: .Machine$double.eps.

MinPeakDistance

Minimum separation between peaks (positive integer). Peaks separated by less than this distance are considered a single peak. This distance is also used to fit a second order polynomial to the peaks to estimate their width, therefore it acts as a smoothing parameter. The neighborhood size is equal to the value of MinPeakDistance. Default: 1.

MinPeakWidth

Minimum width of peaks (positive integer). The width of the peaks is estimated using a parabola fitted to the neighborhood of each peak. The width is calculated with the formula a * (width - x0)^{2} = 1, where a is the the concavity of the parabola and x0 its vertex. Default: 1.

MaxPeakWidth

Maximum width of peaks (positive integer). Default: Inf.

DoubleSided

Tells the function that data takes positive and negative values. The baseline for the peaks is taken as the mean value of the function. This is equivalent as passing the absolute value of the data after removing the mean. Default: FALSE

Details

Peaks of a positive array of data are defined as local maxima. For double-sided data, they are maxima of the positive part and minima of the negative part. data is expected to be a one-dimensional vector.

Value

A list containing the following elements:

pks

The value of data at the peaks.

loc

The index indicating the position of the peaks.

parabol

A list containing the parabola fitted to each returned peak. The list has two fields, x and pp. The field pp contains the coefficients of the 2nd degree polynomial and x the extrema of the interval where it was fitted.

height

The estimated height of the returned peaks (in units of data).

baseline

The height at which the roots of the returned peaks were calculated (in units of data).

roots

The abscissa values (in index units) at which the parabola fitted to each of the returned peaks realizes its width as defined below.

Author(s)

Juan Pablo Carbajal, [e-mail].
Conversion to R by Geert van Boxtel, [e-mail].

Examples

### demo 1
t <- 2 * pi * seq(0, 1,length = 1024)
y <- sin(3.14 * t) + 0.5 * cos(6.09 * t) +
     0.1 * sin(10.11 * t + 1 / 6) + 0.1 * sin(15.3 * t + 1 / 3)

data1 <- abs(y) # Positive values
peaks1 <- findpeaks(data1)

data2 <- y # Double-sided
peaks2 <- findpeaks(data2, DoubleSided = TRUE)
peaks3 <- findpeaks (data2, DoubleSided = TRUE, MinPeakHeight = 0.5)

op <- par(mfrow=c(1,2))
plot(t, data1, type="l", xlab="", ylab="")
points(t[peaks1$loc], peaks1$pks, col = "red", pch = 1)
plot(t, data2, type = "l", xlab = "", ylab = "")
points(t[peaks2$loc], peaks2$pks, col = "red", pch = 1)
points(t[peaks3$loc], peaks3$pks, col = "red", pch = 4)
legend ("topleft", "0: >2*sd, x: >0.5", bty = "n",
        text.col = "red")
par (op)
title("Finding the peaks of smooth data is not a big deal")

## demo 2
t <- 2 * pi * seq(0, 1, length = 1024)
y <- sin(3.14 * t) + 0.5 * cos(6.09 * t) + 0.1 *
     sin(10.11 * t + 1 / 6) + 0.1 * sin(15.3 * t + 1 / 3)
data <- abs(y + 0.1*rnorm(length(y),1))   # Positive values + noise
peaks1 <- findpeaks(data, MinPeakHeight=1)
dt <- t[2]-t[1]
peaks2 <- findpeaks(data, MinPeakHeight=1, MinPeakDistance=round(0.5/dt))
op <- par(mfrow=c(1,2))
plot(t, data, type="l", xlab="", ylab="")
points (t[peaks1$loc],peaks1$pks,col="red", pch=1)
plot(t, data, type="l", xlab="", ylab="")
points (t[peaks2$loc],peaks2$pks,col="red", pch=1)
par (op)
title(paste("Noisy data may need tuning of the parameters.\n",
            "In the 2nd example, MinPeakDistance is used\n",
            "as a smoother of the peaks"))