Package 'alkahest'

Title: Pre-Processing XY Data from Experimental Methods
Description: A lightweight, dependency-free toolbox for pre-processing XY data from experimental methods (i.e. any signal that can be measured along a continuous variable). This package provides methods for baseline estimation and correction, smoothing, normalization, integration and peaks detection. Baseline correction methods includes polynomial fitting as described in Lieber and Mahadevan-Jansen (2003) <doi:10.1366/000370203322554518>, Rolling Ball algorithm after Kneen and Annegarn (1996) <doi:10.1016/0168-583X(95)00908-6>, SNIP algorithm after Ryan et al. (1988) <doi:10.1016/0168-583X(88)90063-8>, 4S Peak Filling after Liland (2015) <doi:10.1016/j.mex.2015.02.009> and more.
Authors: Nicolas Frerebeau [aut, cre] (<https://orcid.org/0000-0001-5759-4944>, Université Bordeaux Montaigne), Brice Lebrun [ctb]
Maintainer: Nicolas Frerebeau <nicolas.frerebeau@u-bordeaux-montaigne.fr>
License: GPL (>= 3)
Version: 1.1.1
Built: 2024-02-18 07:57:01 UTC
Source: CRAN

Help Index


Linear Baseline Estimation

Description

Linear Baseline Estimation

Usage

baseline_linear(x, y, ...)

## S4 method for signature 'numeric,numeric'
baseline_linear(x, y, points = range(x))

## S4 method for signature 'ANY,missing'
baseline_linear(x, points = range(x))

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

points

A numeric vector specifying the data points to be used in the fitting process (in x unit).

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

signal_correct()

Other baseline estimation methods: baseline_peakfilling(), baseline_polynomial(), baseline_rollingball(), baseline_rubberband(), baseline_snip()

Examples

## X-ray diffraction
data("XRD")

## Plot spectrum
plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")

## Linear baseline
baseline <- baseline_linear(XRD, points = c(25, 34))

plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")
lines(baseline, type = "l", col = "red")

## Correct baseline
XRD$count <- XRD$count - baseline$y

plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")

4S Peak Filling

Description

Baseline estimation by iterative mean suppression.

Usage

baseline_peakfilling(x, y, ...)

## S4 method for signature 'numeric,numeric'
baseline_peakfilling(x, y, n, m, by = 10, lambda = 1600, d = 2, sparse = FALSE)

## S4 method for signature 'ANY,missing'
baseline_peakfilling(x, n, m, by = 10, lambda = 1600, d = 2, sparse = FALSE)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

n

An integer value giving the number of iterations.

m

An odd integer giving the half window size.

by

A length-one numeric vector givging the umber of buckets to divide x into.

lambda

An integer giving the smoothing parameter. The larger lambda is, the smoother the curve (see smooth_whittaker()).

d

An integer specifying the order of the penalty (see smooth_whittaker()).

sparse

A logical scalar: should sparse matrices be used for computation (see smooth_whittaker())? If TRUE, Matrix is required.

Author(s)

N. Frerebeau

References

Liland, K. H. (2015). 4S Peak Filling - baseline estimation by iterative mean suppression. MethodsX, 2, 135-140. doi:10.1016/j.mex.2015.02.009.

See Also

signal_correct(), smooth_whittaker()

Other baseline estimation methods: baseline_linear(), baseline_polynomial(), baseline_rollingball(), baseline_rubberband(), baseline_snip()

Examples

## X-ray diffraction
data("XRD")

## 4S Peak Filling baseline
baseline <- baseline_peakfilling(XRD, n = 10, m = 5, by = 10, sparse = TRUE)

plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")
lines(baseline, type = "l", col = "red")

Polynomial Baseline Estimation

Description

Polynomial Baseline Estimation

Usage

baseline_polynomial(x, y, ...)

## S4 method for signature 'numeric,numeric'
baseline_polynomial(x, y, d = 3, tolerance = 0.001, stop = 100)

## S4 method for signature 'ANY,missing'
baseline_polynomial(x, d = 3, tolerance = 0.001, stop = 100)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

d

An integer giving the degree of the polynomial. Must be less than the number of unique points.

tolerance

A numeric scalar giving the tolerance of difference between iterations.

stop

An integer giving the stopping rule (i.e. maximum number of iterations).

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

References

Lieber, C. A. and Mahadevan-Jansen, A. (2003). Automated Method for Subtraction of Fluorescence from Biological Raman Spectra. Applied Spectroscopy, 57(11): 1363-67. doi:10.1366/000370203322554518.

See Also

signal_correct()

Other baseline estimation methods: baseline_linear(), baseline_peakfilling(), baseline_rollingball(), baseline_rubberband(), baseline_snip()

Examples

## X-ray diffraction
data("XRD")

## Subset from 20 to 70 degrees
XRD <- signal_select(XRD, from = 20, to = 70)

## Plot spectrum
plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")

## Polynomial baseline
baseline <- baseline_polynomial(XRD, d = 4, tolerance = 0.02, stop = 1000)

plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")
lines(baseline, type = "l", col = "red")

Rolling Ball Baseline Estimation

Description

Rolling Ball Baseline Estimation

Usage

baseline_rollingball(x, y, ...)

## S4 method for signature 'numeric,numeric'
baseline_rollingball(x, y, m, s)

## S4 method for signature 'ANY,missing'
baseline_rollingball(x, m, s)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

m

An odd integer giving the window size (i.e. the number of adjacent points to be used; see window_sliding()) for minimization/maximization.

s

An odd integer giving the window size (i.e. the number of adjacent points to be used; see window_sliding()) for smoothing.

Value

Returns a list with two components x and y.

Note

There will be (m1)/2(m - 1) / 2 points both at the beginning and at the end of the data series for which a complete mm-width window cannot be obtained. To prevent data loss, progressively wider/narrower windows are used at both ends of the data series.

Author(s)

N. Frerebeau

References

Kneen, M. A. and Annegarn, H. J. (1996). Algorithm for Fitting XRF, SEM and PIXE X-Ray Spectra Backgrounds. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 109/110: 209-213. doi:10.1016/0168-583X(95)00908-6.

See Also

signal_correct()

Other baseline estimation methods: baseline_linear(), baseline_peakfilling(), baseline_polynomial(), baseline_rubberband(), baseline_snip()

Examples

## X-ray diffraction
data("XRD")

## Subset from 20 to 70 degrees
XRD <- signal_select(XRD, from = 20, to = 70)

## Plot spectrum
plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")

## Rolling Ball baseline
baseline <- baseline_rollingball(XRD, m = 201, s = 151)

plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")
lines(baseline, type = "l", col = "red")

Rubberband Baseline Estimation

Description

Rubberband Baseline Estimation

Usage

baseline_rubberband(x, y, ...)

## S4 method for signature 'numeric,numeric'
baseline_rubberband(x, y, noise = 0, spline = TRUE, ...)

## S4 method for signature 'ANY,missing'
baseline_rubberband(x, noise = 0, spline = TRUE, ...)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Extra arguments to be passed to stats::smooth.spline().

noise

A length-one numeric vector giving the noise level. Only used if method is "rubberband".

spline

A logical scalar: should spline interpolation through the support points be used instead of linear interpolation? Only used if method is "rubberband".

Details

A convex envelope of the spectrum is determined and the baseline is estimated as the part of the convex envelope lying below the spectrum. Note that the rubber band does not enter the concave regions (if any) of the spectrum.

Value

Returns a list with two components x and y.

Note

baseline_rubberband() is slightly modified from C. Beleites' hyperSpec::spc.rubberband().

Author(s)

N. Frerebeau

See Also

signal_correct()

Other baseline estimation methods: baseline_linear(), baseline_peakfilling(), baseline_polynomial(), baseline_rollingball(), baseline_snip()

Examples

## gamma-ray spectrometry
data("BEGe")

## Subset from 2.75 to 200 keV
BEGe <- signal_select(BEGe, from = 3, to = 200)

## Plot spectrum
plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")

## Rubberband baseline
baseline <- baseline_rubberband(BEGe)

plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")
lines(baseline, type = "l", col = "red")

SNIP Baseline Estimation

Description

Sensitive Nonlinear Iterative Peak clipping algorithm.

Usage

baseline_snip(x, y, ...)

## S4 method for signature 'numeric,numeric'
baseline_snip(x, y, LLS = FALSE, decreasing = FALSE, n = 100)

## S4 method for signature 'ANY,missing'
baseline_snip(x, LLS = FALSE, decreasing = FALSE, n = 100)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

LLS

A logical scalar: should the LLS operator be applied on x before employing SNIP algorithm? Only used if method is "SNIP".

decreasing

A logical scalar: should a decreasing clipping window be used?

n

An integer value giving the number of iterations.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

References

Morháč, M., Kliman, J., Matoušek, V., Veselský, M. & Turzo, I. (1997). Background elimination methods for multidimensional gamma-ray spectra. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 401(1), p. 113-132. doi:10.1016/S0168-9002(97)01023-1

Morháč, M. & Matoušek, V. (2008). Peak Clipping Algorithms for Background Estimation in Spectroscopic Data. Applied Spectroscopy, 62(1), p. 91-106. doi:10.1366/000370208783412762

Ryan, C. G., Clayton, E., Griffin, W. L., Sie, S. H. & Cousens, D. R. (1988). SNIP, a statistics-sensitive background treatment for the quantitative analysis of PIXE spectra in geoscience applications. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 34(3), p. 396-402. doi:10.1016/0168-583X(88)90063-8

See Also

signal_correct()

Other baseline estimation methods: baseline_linear(), baseline_peakfilling(), baseline_polynomial(), baseline_rollingball(), baseline_rubberband()

Examples

## gamma-ray spectrometry
data("BEGe")

## Subset from 2.75 to 200 keV
BEGe <- signal_select(BEGe, from = 3, to = 200)

## Plot spectrum
plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")

## SNIP baseline
baseline <- baseline_snip(BEGe, LLS = FALSE, decreasing = FALSE, n = 100)

plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")
lines(baseline, type = "l", col = "red")

Gamma-Ray Spectrometry

Description

Gamma-Ray Spectrometry

Usage

BEGe

Format

A data.frame with 8192 rows (channels) and 2 variables.

energy

(keV)

count

See Also

Other datasets: LaBr, XRD

Examples

data("BEGe")
plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")

Rectangle Rule

Description

Approximates the definite integral by using the rectangle rule.

Usage

integrate_rectangle(x, y, ...)

## S4 method for signature 'numeric,numeric'
integrate_rectangle(x, y, right = FALSE)

## S4 method for signature 'ANY,missing'
integrate_rectangle(x, right = FALSE)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

right

A logical scalar: should the right rule be used instead of the left rule?

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other integration methods: integrate_trapezoid()

Examples

## Calculate the area under the sine curve from 0 to pi
# integrate(f = function(x) x^3, lower = 0, upper = 2)
x <- seq(0, 2, len = 101)
y <- x^3

plot(x, y, type = "l")

integrate_rectangle(x, y, right = FALSE) # 3.9204
integrate_rectangle(x, y, right = TRUE) # 4.0804
integrate_trapezoid(x, y) # 4.0004

Trapezoidal Rule

Description

Approximates the definite integral by using the trapezoidal rule.

Usage

integrate_trapezoid(x, y, ...)

## S4 method for signature 'numeric,numeric'
integrate_trapezoid(x, y)

## S4 method for signature 'ANY,missing'
integrate_trapezoid(x)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other integration methods: integrate_rectangle()

Examples

## Calculate the area under the sine curve from 0 to pi
# integrate(f = function(x) x^3, lower = 0, upper = 2)
x <- seq(0, 2, len = 101)
y <- x^3

plot(x, y, type = "l")

integrate_rectangle(x, y, right = FALSE) # 3.9204
integrate_rectangle(x, y, right = TRUE) # 4.0804
integrate_trapezoid(x, y) # 4.0004

Strip XRD ka2

Description

Strip XRD ka2

Usage

ka2_strip_penalized(x, y, ...)

## S4 method for signature 'numeric,numeric'
ka2_strip_penalized(
  x,
  y,
  lambda,
  wave = c(1.5406, 1.54443),
  tau = 0.5,
  nseg = 1,
  progress = interactive()
)

## S4 method for signature 'ANY,missing'
ka2_strip_penalized(
  x,
  lambda,
  wave = c(1.5406, 1.54443),
  tau = 0.5,
  nseg = 1,
  progress = interactive()
)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

lambda

An integer giving the smoothing parameter. The larger lambda is, the smoother the curve.

wave

A length-two numeric vector giving the characteristic wavelengths of the anode material (defaults to copper).

tau

A length-one numeric vector giving the ratio between α\alpha1 and α\alpha2 line intensities (defaults to 1/2).

nseg

A length-one numeric vector specifying the number of equally sized segments for B-spline basis matrix computation.

progress

A logical scalar: should a progress bar be displayed?

Value

Returns a list with two components x and y.

Note

Matrix is required.

Author(s)

J. J. de Rooi et al. (original R code).

References

de Rooi, J. J., van der Pers, N. M., Hendrikx, R. W. A., Delhez, R., Böttger A. J. and Eilers, P. H. C. (2014). Smoothing of X-ray diffraction data and Ka2 elimination using penalized likelihood and the composite link model. Journal of Applied Crystallography, 47: 852-860. doi:10.1107/S1600576714005809

Examples

## Not run: 
## X-ray diffraction
data("XRD")

## Subset from 20 to 40 degrees
XRD <- signal_select(XRD, from = 20, to = 40)

## Plot diffractogram
plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")

## Penalized likelihood smoothing
lambda <- seq(from = 1, to = 8, length.out = 40)
lambda <- 10^lambda

likelihood <- smooth_likelihood(XRD, lambda = lambda, d = 3)
lines(likelihood, col = "red")

## Strip ka2
ka2 <- ka2_strip_penalized(XRD, lambda = lambda, tau = 0.5, nseg = 1)
lines(ka2, col = "blue")

## End(Not run)

Gamma-Ray Spectrometry

Description

Gamma-Ray Spectrometry

Usage

LaBr

Format

A data.frame with 1024 rows (channels) and 2 variables.

energy

(keV)

count

See Also

Other datasets: BEGe, XRD

Examples

data("LaBr")
plot(LaBr, type = "l", xlab = "Energy (keV)", ylab = "Count")

Find Peaks

Description

Finds local maxima in sequential data.

Usage

peaks_find(x, y, ...)

## S4 method for signature 'numeric,numeric'
peaks_find(x, y, method = "MAD", SNR = 2, m = NULL, ...)

## S4 method for signature 'ANY,missing'
peaks_find(x, method = "MAD", SNR = 2, m = NULL, ...)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Extra parameters to be passed to internal methods.

method

A character string specifying the method to be used for background noise estimation (see below).

SNR

An integer giving the signal-to-noise-ratio for peak detection (see below).

m

An odd integer giving the window size (i.e. the number of adjacent points to be used). If NULL, 5% of the data points is used as the half window size.

Details

A local maximum has to be the highest one in the given window and has to be higher than SNR×noiseSNR \times noise to be recognized as peak.

The following methods are available for noise estimation:

MAD

Median Absolute Deviation.

Note that to improve peak detection, it may be helpful to smooth the data and remove the baseline beforehand.

Value

Returns a list with two components x and y.

Note

There will be (m1)/2(m - 1) / 2 points both at the beginning and at the end of the data series for which a complete mm-width window cannot be obtained. To prevent data loss, progressively wider/narrower windows are used at both ends of the data series.

Adapted from Stasia Grinberg's findPeaks function.

Author(s)

N. Frerebeau

See Also

Other peaks detection methods: peaks_fwhm()

Examples

## X-ray diffraction
data("XRD")

## 4S Peak Filling baseline
baseline <- baseline_peakfilling(XRD, n = 10, m = 5, by = 10, sparse = TRUE)

plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")
lines(baseline, type = "l", col = "red")

## Correct baseline
XRD <- signal_drift(XRD, lag = baseline, subtract = TRUE)

## Find peaks
peaks <- peaks_find(XRD, SNR = 3, m = 11)

plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")
lines(peaks, type = "p", pch = 16, col = "red")
abline(h = attr(peaks, "noise"), lty = 2) # noise threshold

## Half-Width at Half-Maximum
x <- seq(-4, 4, length = 1000)
y <- dnorm(x)

peaks_fwhm(x, y, center = 0) # Expected: 2 * sqrt(2 * log(2))

Half-Width at Half-Maximum

Description

Estimates the Half-Width at Half-Maximum (FWHM) for a given peak.

Usage

peaks_fwhm(x, y, ...)

## S4 method for signature 'numeric,numeric'
peaks_fwhm(x, y, center)

## S4 method for signature 'ANY,missing'
peaks_fwhm(x, center)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

center

A numeric value giving the peak position in x units.

Details

It tries to get the smallest possible estimate.

Value

A numeric value.

Author(s)

N. Frerebeau

See Also

Other peaks detection methods: peaks_find()

Examples

## X-ray diffraction
data("XRD")

## 4S Peak Filling baseline
baseline <- baseline_peakfilling(XRD, n = 10, m = 5, by = 10, sparse = TRUE)

plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")
lines(baseline, type = "l", col = "red")

## Correct baseline
XRD <- signal_drift(XRD, lag = baseline, subtract = TRUE)

## Find peaks
peaks <- peaks_find(XRD, SNR = 3, m = 11)

plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")
lines(peaks, type = "p", pch = 16, col = "red")
abline(h = attr(peaks, "noise"), lty = 2) # noise threshold

## Half-Width at Half-Maximum
x <- seq(-4, 4, length = 1000)
y <- dnorm(x)

peaks_fwhm(x, y, center = 0) # Expected: 2 * sqrt(2 * log(2))

Replace Negative Values

Description

Replace Negative Values

Usage

replace_negative(x, y, ...)

## S4 method for signature 'numeric,numeric'
replace_negative(x, y, value = 0)

## S4 method for signature 'ANY,missing'
replace_negative(x, value = 0)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Extra parameters to be passed to threshold.

value

A numeric value to replace negative values.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other replacement methods: replace_threshold()


Replace Values Below a Given Threshold

Description

Replace Values Below a Given Threshold

Usage

replace_threshold(x, y, threshold, ...)

## S4 method for signature 'numeric,numeric,'function''
replace_threshold(x, y, threshold, value = 0, ...)

## S4 method for signature 'ANY,missing,'function''
replace_threshold(x, threshold, value = 0, ...)

## S4 method for signature 'numeric,numeric,numeric'
replace_threshold(x, y, threshold, value = 0, ...)

## S4 method for signature 'ANY,missing,numeric'
replace_threshold(x, threshold, value = 0, ...)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

threshold

A numeric value or a function that takes a numeric vector as argument and returns a single numeric value.

...

Extra parameters to be passed to threshold.

value

A numeric value to replace values below threshold.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other replacement methods: replace_negative()


Bin

Description

Averages x values and applies a function to the corresponding y values.

Usage

resample_bin(x, y, ...)

## S4 method for signature 'numeric,numeric'
resample_bin(x, y, by, f = mean, ...)

## S4 method for signature 'ANY,missing'
resample_bin(x, y, by, f = sum)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Extra parameters to be passed to f.

by

An integer specifying the binning ratio (i.e. the number of points to be grouped together; see window_tumbling()).

f

A function that takes a numeric vector of intensities as argument and returns a single numeric vector. Used to estimate the local representative value in each bin (defaults to sum(); see examples).

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other resampling methods: resample_down(), resample_interpolate()

Examples

## X-ray diffraction
data("XRD")

## Plot spectrum
plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")

## Bin by 3
XRD_bin_mean <- resample_bin(XRD, by = 3, f = mean)
XRD_bin_min <- resample_bin(XRD, by = 3, f = min)

plot(XRD, type = "l", xlim = c(25, 35),
     xlab = expression(2*theta), ylab = "Count")
lines(XRD_bin_mean, type = "l", col = "red")
lines(XRD_bin_min, type = "l", col = "green")

## Downsample by 10
XRD_down <- resample_down(XRD, by = 10)

plot(XRD, type = "l", xlim = c(20, 40),
     xlab = expression(2*theta), ylab = "Count")
lines(XRD_down, type = "l", col = "red")

## Linearly interpolate
XRD_approx <- resample_interpolate(XRD, from = 20, to = 40, by = 0.02)

plot(XRD, type = "l", xlim = c(20, 40),
     xlab = expression(2*theta), ylab = "Count")
lines(XRD_approx, type = "l", col = "red")

Downsample

Description

Downsample

Usage

resample_down(x, y, ...)

## S4 method for signature 'numeric,numeric'
resample_down(x, y, by)

## S4 method for signature 'ANY,missing'
resample_down(x, y, by)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

by

An integer specifying the downsampling factor.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other resampling methods: resample_bin(), resample_interpolate()

Examples

## X-ray diffraction
data("XRD")

## Plot spectrum
plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")

## Bin by 3
XRD_bin_mean <- resample_bin(XRD, by = 3, f = mean)
XRD_bin_min <- resample_bin(XRD, by = 3, f = min)

plot(XRD, type = "l", xlim = c(25, 35),
     xlab = expression(2*theta), ylab = "Count")
lines(XRD_bin_mean, type = "l", col = "red")
lines(XRD_bin_min, type = "l", col = "green")

## Downsample by 10
XRD_down <- resample_down(XRD, by = 10)

plot(XRD, type = "l", xlim = c(20, 40),
     xlab = expression(2*theta), ylab = "Count")
lines(XRD_down, type = "l", col = "red")

## Linearly interpolate
XRD_approx <- resample_interpolate(XRD, from = 20, to = 40, by = 0.02)

plot(XRD, type = "l", xlim = c(20, 40),
     xlab = expression(2*theta), ylab = "Count")
lines(XRD_approx, type = "l", col = "red")

Linearly Interpolate

Description

Linearly Interpolate

Usage

resample_interpolate(x, y, ...)

## S4 method for signature 'numeric,numeric'
resample_interpolate(x, y, from, to, by, ...)

## S4 method for signature 'ANY,missing'
resample_interpolate(x, y, from, to, by, ...)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Extra arguments to be passed to stats::approx().

from

A length-one numeric vector giving the starting value of the sequence where interpolation is to take place.

to

A length-one numeric vector giving the end value of the sequence where interpolation is to take place.

by

A length-one numeric vector specifying the increment of the sequence.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other resampling methods: resample_bin(), resample_down()

Examples

## X-ray diffraction
data("XRD")

## Plot spectrum
plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")

## Bin by 3
XRD_bin_mean <- resample_bin(XRD, by = 3, f = mean)
XRD_bin_min <- resample_bin(XRD, by = 3, f = min)

plot(XRD, type = "l", xlim = c(25, 35),
     xlab = expression(2*theta), ylab = "Count")
lines(XRD_bin_mean, type = "l", col = "red")
lines(XRD_bin_min, type = "l", col = "green")

## Downsample by 10
XRD_down <- resample_down(XRD, by = 10)

plot(XRD, type = "l", xlim = c(20, 40),
     xlab = expression(2*theta), ylab = "Count")
lines(XRD_down, type = "l", col = "red")

## Linearly interpolate
XRD_approx <- resample_interpolate(XRD, from = 20, to = 40, by = 0.02)

plot(XRD, type = "l", xlim = c(20, 40),
     xlab = expression(2*theta), ylab = "Count")
lines(XRD_approx, type = "l", col = "red")

Normalize intensities by AUC

Description

Rescales intensities so that the area under the curve (AUC) is equal to 1.

Usage

rescale_area(x, y, ...)

## S4 method for signature 'numeric,numeric'
rescale_area(x, y, method = c("rectangle", "trapezoid"), ...)

## S4 method for signature 'ANY,missing'
rescale_area(x, method = c("rectangle", "trapezoid"), ...)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

method

A character string specifying the method for integration. It must be one of "rectangle" or "trapezoid". Any unambiguous substring can be given.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other normalization methods: rescale_range(), rescale_total(), rescale_transform()

Examples

## gamma-ray spectrometry
data("BEGe")

## Subset from 2.75 to 200 keV
BEGe <- signal_select(BEGe, from = 3, to = 200)

## Plot spectrum
plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")

## Normalize by area under the curve
BEGe_area <- rescale_area(BEGe)
plot(BEGe_area, type = "l", xlab = "Energy (keV)", ylab = "Count")
integrate_rectangle(BEGe)
integrate_rectangle(BEGe_area)

## Rescale so that intensities sum to 1
BEGe_total <- rescale_total(BEGe, total = 1)
plot(BEGe_total, type = "l", xlab = "Energy (keV)", ylab = "Count")

## Rescale intensities to 0-1
BEGe_range <- rescale_range(BEGe, min = 0, max = 1)
plot(BEGe_range, type = "l", xlab = "Energy (keV)", ylab = "Count")

Rescales intensities to have specified minimum and maximum

Description

Rescales intensities to have specified minimum and maximum.

Usage

rescale_range(x, y, ...)

rescale_min(x, y, ...)

rescale_max(x, y, ...)

## S4 method for signature 'numeric,numeric'
rescale_range(x, y, min = 0, max = 1)

## S4 method for signature 'ANY,missing'
rescale_range(x, min = 0, max = 1)

## S4 method for signature 'numeric,numeric'
rescale_min(x, y, min = 0)

## S4 method for signature 'ANY,missing'
rescale_min(x, min = 0)

## S4 method for signature 'numeric,numeric'
rescale_max(x, y, max = 1)

## S4 method for signature 'ANY,missing'
rescale_max(x, max = 1)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

min

A legnth-one numeric vector specifying the output minimum.

max

A legnth-one numeric vector specifying the output maximum.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other normalization methods: rescale_area(), rescale_total(), rescale_transform()

Examples

## gamma-ray spectrometry
data("BEGe")

## Subset from 2.75 to 200 keV
BEGe <- signal_select(BEGe, from = 3, to = 200)

## Plot spectrum
plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")

## Normalize by area under the curve
BEGe_area <- rescale_area(BEGe)
plot(BEGe_area, type = "l", xlab = "Energy (keV)", ylab = "Count")
integrate_rectangle(BEGe)
integrate_rectangle(BEGe_area)

## Rescale so that intensities sum to 1
BEGe_total <- rescale_total(BEGe, total = 1)
plot(BEGe_total, type = "l", xlab = "Energy (keV)", ylab = "Count")

## Rescale intensities to 0-1
BEGe_range <- rescale_range(BEGe, min = 0, max = 1)
plot(BEGe_range, type = "l", xlab = "Energy (keV)", ylab = "Count")

Rescale intensities to sum to a specified value

Description

Rescales intensities to sum to a specified value.

Usage

rescale_total(x, y, ...)

## S4 method for signature 'numeric,numeric'
rescale_total(x, y, total = 1)

## S4 method for signature 'ANY,missing'
rescale_total(x, total = 1)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

total

A legnth-one numeric vector specifying the output total. Defaults to 1, i.e. normalizes by total intensity.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other normalization methods: rescale_area(), rescale_range(), rescale_transform()

Examples

## gamma-ray spectrometry
data("BEGe")

## Subset from 2.75 to 200 keV
BEGe <- signal_select(BEGe, from = 3, to = 200)

## Plot spectrum
plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")

## Normalize by area under the curve
BEGe_area <- rescale_area(BEGe)
plot(BEGe_area, type = "l", xlab = "Energy (keV)", ylab = "Count")
integrate_rectangle(BEGe)
integrate_rectangle(BEGe_area)

## Rescale so that intensities sum to 1
BEGe_total <- rescale_total(BEGe, total = 1)
plot(BEGe_total, type = "l", xlab = "Energy (keV)", ylab = "Count")

## Rescale intensities to 0-1
BEGe_range <- rescale_range(BEGe, min = 0, max = 1)
plot(BEGe_range, type = "l", xlab = "Energy (keV)", ylab = "Count")

Transform Intensities

Description

Transform Intensities

Usage

rescale_transform(x, y, ...)

## S4 method for signature 'numeric,numeric'
rescale_transform(x, y, f, ...)

## S4 method for signature 'ANY,missing'
rescale_transform(x, f, ...)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Extra arguments to be passed to f.

f

A function that takes a numeric vector of intensities as argument and returns a numeric vector.

Details

Transformation of intensities can be used to improve the identification of peaks with a low signal-to-noise ratio.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other normalization methods: rescale_area(), rescale_range(), rescale_total()

Examples

## gamma-ray spectrometry
data("BEGe")

## Subset from 2.75 to 200 keV
BEGe <- signal_select(BEGe, from = 3, to = 200)

## Plot spectrum
plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")

## Transform intensities
BEGe_trans <- rescale_transform(BEGe, f = sqrt)
plot(BEGe_trans, type = "l", xlab = "Energy (keV)", ylab = "sqrt(Count)")

Bind

Description

Combines XY objects.

Usage

signal_bind(...)

## S4 method for signature 'ANY'
signal_bind(...)

Arguments

...

Any object that can be interpreted in a suitable way (see grDevices::xy.coords()).

Value

Returns a matrix of intensities.

Author(s)

N. Frerebeau

See Also

Other signal processing methods: signal_correct(), signal_drift(), signal_mean(), signal_shift(), subset()

Examples

## X-ray diffraction
data("XRD")

XRD1 <- signal_drift(XRD, lag = 1500)

## Bind
XRD_bind <- signal_bind(XRD, XRD1)
XRD_bind[, 1:10]

## Mean
XRD_mean <- signal_mean(XRD, XRD1)

plot(NULL, type = "l", xlim = c(10, 70) , ylim = c(3000, 36000),
     xlab = expression(2*theta), ylab = "Count")
lines(XRD, type = "l")
lines(XRD1, type = "l")
lines(XRD_mean, type = "l", col = "red")

Baseline Correction

Description

Baseline Correction

Usage

signal_correct(x, y, ...)

## S4 method for signature 'numeric,numeric'
signal_correct(x, y, method = c("linear", "rubberband", "SNIP", "4S"), ...)

## S4 method for signature 'ANY,missing'
signal_correct(x, method = c("linear", "rubberband", "SNIP", "4S"), ...)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Extra arguments to be passed to ⁠baseline_*()⁠ (see details).

method

A character string specifying the method for baseline estimation. It must be one of "linear", "rubberband", "SNIP" or "⁠4S⁠" (see details). Any unambiguous substring can be given.

Details

Available methods for baseline estimation:

linear

Linear baseline estimation (see baseline_linear()).

rubberband

Rubberband baseline estimation (see baseline_rubberband()).

SNIP

Sensitive Nonlinear Iterative Peak clipping algorithm (see baseline_snip()).

⁠4S⁠

4S Peak Filling (see baseline_peakfilling()).

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other signal processing methods: signal_bind(), signal_drift(), signal_mean(), signal_shift(), subset()

Examples

## gamma-ray spectrometry
data("BEGe")

## Subset from 2.75 to 200 keV
BEGe <- signal_select(BEGe, from = 3, to = 200)

## Drift
baseline <- baseline_snip(BEGe)
BEGe_drif <- signal_drift(BEGe, lag = baseline, subtract = TRUE)

plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")
lines(BEGe_drif, type = "l", col = "red")

## Correct
BEGe_corr <- signal_correct(BEGe, method = "SNIP")

plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")
lines(BEGe_corr, type = "l", col = "red")

Drift Intensities

Description

Drift Intensities

Usage

signal_drift(x, y, lag, ...)

## S4 method for signature 'numeric,numeric,numeric'
signal_drift(x, y, lag)

## S4 method for signature 'ANY,missing,ANY'
signal_drift(x, lag, subtract = FALSE)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

lag

A numeric vector specifying the offset or any object that can be interpreted in a suitable way (see grDevices::xy.coords())

...

Currently not used.

subtract

A logical scalar: should lag be subtracted to y?

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other signal processing methods: signal_bind(), signal_correct(), signal_mean(), signal_shift(), subset()

Examples

## gamma-ray spectrometry
data("BEGe")

## Subset from 2.75 to 200 keV
BEGe <- signal_select(BEGe, from = 3, to = 200)

## Drift
BEGe_plus <- signal_drift(BEGe, lag = 250)
BEGe_minus <- signal_drift(BEGe, lag = 250, subtract = TRUE)

plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")
lines(BEGe_plus, type = "l", col = "red")
lines(BEGe_minus, type = "l", col = "green")

Mean Intensities

Description

Mean Intensities

Usage

signal_mean(...)

## S4 method for signature 'ANY'
signal_mean(...)

Arguments

...

Any object that can be interpreted in a suitable way (see grDevices::xy.coords()).

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other signal processing methods: signal_bind(), signal_correct(), signal_drift(), signal_shift(), subset()

Examples

## X-ray diffraction
data("XRD")

XRD1 <- signal_drift(XRD, lag = 1500)

## Bind
XRD_bind <- signal_bind(XRD, XRD1)
XRD_bind[, 1:10]

## Mean
XRD_mean <- signal_mean(XRD, XRD1)

plot(NULL, type = "l", xlim = c(10, 70) , ylim = c(3000, 36000),
     xlab = expression(2*theta), ylab = "Count")
lines(XRD, type = "l")
lines(XRD1, type = "l")
lines(XRD_mean, type = "l", col = "red")

Shift the X Scale

Description

Shifts the x scale by a given value.

Usage

signal_shift(x, y, lag, ...)

## S4 method for signature 'numeric,numeric'
signal_shift(x, y, lag)

## S4 method for signature 'ANY,missing'
signal_shift(x, lag)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

lag

A numeric vector specifying the offset.

...

Currently not used.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other signal processing methods: signal_bind(), signal_correct(), signal_drift(), signal_mean(), subset()

Examples

## X-ray diffraction
data("XRD")

## Plot spectrum
plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")

## Shift by one degree
XRD_offset <- signal_shift(XRD, lag = 1)
lines(XRD_offset, type = "l", col = "red")

Penalized Likelihood Smoothing

Description

Penalized Likelihood Smoothing

Usage

smooth_likelihood(x, y, ...)

## S4 method for signature 'numeric,numeric'
smooth_likelihood(x, y, lambda, d = 2, SE = FALSE, progress = interactive())

## S4 method for signature 'ANY,missing'
smooth_likelihood(x, lambda, d = 2, SE = FALSE, progress = interactive())

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

lambda

An integer giving the smoothing parameter. The larger lambda is, the smoother the curve.

d

An integer specifying the order of the penalty.

SE

A logical scalar: should standard errors be returned?

progress

A logical scalar: should a progress bar be displayed?

Value

Returns a list with two components x and y.

Note

Matrix is required.

Author(s)

J. J. de Rooi et al. (original R code).

References

de Rooi, J. J., van der Pers, N. M., Hendrikx, R. W. A., Delhez, R., Böttger A. J. and Eilers, P. H. C. (2014). Smoothing of X-ray diffraction data and Ka2 elimination using penalized likelihood and the composite link model. Journal of Applied Crystallography, 47: 852-860. doi:10.1107/S1600576714005809

See Also

Other smoothing methods: smooth_loess(), smooth_rectangular(), smooth_savitzky(), smooth_triangular(), smooth_whittaker()

Examples

## Not run: 
## X-ray diffraction
data("XRD")

## Subset from 20 to 40 degrees
XRD <- signal_select(XRD, from = 20, to = 40)

## Plot diffractogram
plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")

## Penalized likelihood smoothing
lambda <- seq(from = 1, to = 8, length.out = 40)
lambda <- 10^lambda

likelihood <- smooth_likelihood(XRD, lambda = lambda, d = 3)
lines(likelihood, col = "red")

## Strip ka2
ka2 <- ka2_strip_penalized(XRD, lambda = lambda, tau = 0.5, nseg = 1)
lines(ka2, col = "blue")

## End(Not run)

Loess Smoothing

Description

Smoothes intensities by loess fitting.

Usage

smooth_loess(x, y, ...)

## S4 method for signature 'numeric,numeric'
smooth_loess(x, y, span = 0.75, ...)

## S4 method for signature 'ANY,missing'
smooth_loess(x, span = 0.75, ...)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Extra arguments to be passed to stats::loess().

span

An integer specifying the degree of smoothing (see stats::loess()).

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other smoothing methods: smooth_likelihood(), smooth_rectangular(), smooth_savitzky(), smooth_triangular(), smooth_whittaker()

Examples

## Simulate data with some noise
x <- seq(-4, 4, length = 100)
y <- dnorm(x) + rnorm(100, mean = 0, sd = 0.01)

## Plot spectrum
plot(x, y, type = "l", xlab = "", ylab = "")

## Rectangular smoothing
unweighted <- smooth_rectangular(x, y, m = 3)
plot(unweighted, type = "l", xlab = "", ylab = "")

## Triangular smoothing
weighted <- smooth_triangular(x, y, m = 5)
plot(weighted, type = "l", xlab = "", ylab = "")

## Loess smoothing
loess <- smooth_loess(x, y, span = 0.75)
plot(loess, type = "l", xlab = "", ylab = "")

## Savitzky–Golay filter
savitzky <- smooth_savitzky(x, y, m = 21, p = 2)
plot(savitzky, type = "l", xlab = "", ylab = "")

## Whittaker smoothing
whittaker <- smooth_whittaker(x, y, lambda = 1600, d = 2)
plot(whittaker, type = "l", xlab = "", ylab = "")

Rectangular Smoothing

Description

Unweighted sliding-average or rectangular Smoothing.

Usage

smooth_rectangular(x, y, ...)

## S4 method for signature 'numeric,numeric'
smooth_rectangular(x, y, m = 3)

## S4 method for signature 'ANY,missing'
smooth_rectangular(x, m)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

m

An odd integer giving the window size (i.e. the number of adjacent points to be used; see window_sliding()).

Details

It replaces each point in the signal with the average of mm adjacent points.

Value

Returns a list with two components x and y.

Note

There will be (m1)/2(m - 1) / 2 points both at the beginning and at the end of the data series for which a complete mm-width window cannot be obtained. To prevent data loss, progressively wider/narrower windows are used at both ends of the data series.

Author(s)

N. Frerebeau

See Also

Other smoothing methods: smooth_likelihood(), smooth_loess(), smooth_savitzky(), smooth_triangular(), smooth_whittaker()

Examples

## Simulate data with some noise
x <- seq(-4, 4, length = 100)
y <- dnorm(x) + rnorm(100, mean = 0, sd = 0.01)

## Plot spectrum
plot(x, y, type = "l", xlab = "", ylab = "")

## Rectangular smoothing
unweighted <- smooth_rectangular(x, y, m = 3)
plot(unweighted, type = "l", xlab = "", ylab = "")

## Triangular smoothing
weighted <- smooth_triangular(x, y, m = 5)
plot(weighted, type = "l", xlab = "", ylab = "")

## Loess smoothing
loess <- smooth_loess(x, y, span = 0.75)
plot(loess, type = "l", xlab = "", ylab = "")

## Savitzky–Golay filter
savitzky <- smooth_savitzky(x, y, m = 21, p = 2)
plot(savitzky, type = "l", xlab = "", ylab = "")

## Whittaker smoothing
whittaker <- smooth_whittaker(x, y, lambda = 1600, d = 2)
plot(whittaker, type = "l", xlab = "", ylab = "")

Savitzky-Golay Filter

Description

Savitzky-Golay Filter

Usage

smooth_savitzky(x, y, ...)

## S4 method for signature 'numeric,numeric'
smooth_savitzky(x, y, m = 3, p = 2)

## S4 method for signature 'ANY,missing'
smooth_savitzky(x, m, p)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

m

An odd integer giving the window size (i.e. the number of adjacent points to be used).

p

An integer giving the degree of the polynomial to be used.

Details

This method is based on the least-squares fitting of polynomials to segments of mm adjacent points.

Value

Returns a list with two components x and y.

Note

There will be (m1)/2(m - 1) / 2 points both at the beginning and at the end of the data series for which a complete mm-width window cannot be obtained. To prevent data loss, the original (m1)/2(m - 1) / 2 points at both ends of the data series are preserved.

Author(s)

N. Frerebeau

References

Gorry, P. A. (1990). General Least-Squares Smoothing and Differentiation by the Convolution (Savitzky-Golay) Method. Analytical Chemistry, 62(6), p. 570-573. doi:10.1021/ac00205a007.

Savitzky, A. & Golay, M. J. E. (1964). Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 36(8), p. 1627-1639. doi:10.1021/ac60214a047.

See Also

Other smoothing methods: smooth_likelihood(), smooth_loess(), smooth_rectangular(), smooth_triangular(), smooth_whittaker()

Examples

## Simulate data with some noise
x <- seq(-4, 4, length = 100)
y <- dnorm(x) + rnorm(100, mean = 0, sd = 0.01)

## Plot spectrum
plot(x, y, type = "l", xlab = "", ylab = "")

## Rectangular smoothing
unweighted <- smooth_rectangular(x, y, m = 3)
plot(unweighted, type = "l", xlab = "", ylab = "")

## Triangular smoothing
weighted <- smooth_triangular(x, y, m = 5)
plot(weighted, type = "l", xlab = "", ylab = "")

## Loess smoothing
loess <- smooth_loess(x, y, span = 0.75)
plot(loess, type = "l", xlab = "", ylab = "")

## Savitzky–Golay filter
savitzky <- smooth_savitzky(x, y, m = 21, p = 2)
plot(savitzky, type = "l", xlab = "", ylab = "")

## Whittaker smoothing
whittaker <- smooth_whittaker(x, y, lambda = 1600, d = 2)
plot(whittaker, type = "l", xlab = "", ylab = "")

Triangular Smoothing

Description

Weighted sliding-average or triangular smoothing.

Usage

smooth_triangular(x, y, ...)

## S4 method for signature 'numeric,numeric'
smooth_triangular(x, y, m = 3)

## S4 method for signature 'ANY,missing'
smooth_triangular(x, m)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

m

An odd integer giving the window size (i.e. the number of adjacent points to be used; see window_sliding()).

Details

It replaces each point in the signal with the weighted mean of mm adjacent points.

Value

Returns a list with two components x and y.

Note

There will be (m1)/2(m - 1) / 2 points both at the beginning and at the end of the data series for which a complete mm-width window cannot be obtained. To prevent data loss, progressively wider/narrower windows are used at both ends of the data series.

Author(s)

N. Frerebeau

See Also

Other smoothing methods: smooth_likelihood(), smooth_loess(), smooth_rectangular(), smooth_savitzky(), smooth_whittaker()

Examples

## Simulate data with some noise
x <- seq(-4, 4, length = 100)
y <- dnorm(x) + rnorm(100, mean = 0, sd = 0.01)

## Plot spectrum
plot(x, y, type = "l", xlab = "", ylab = "")

## Rectangular smoothing
unweighted <- smooth_rectangular(x, y, m = 3)
plot(unweighted, type = "l", xlab = "", ylab = "")

## Triangular smoothing
weighted <- smooth_triangular(x, y, m = 5)
plot(weighted, type = "l", xlab = "", ylab = "")

## Loess smoothing
loess <- smooth_loess(x, y, span = 0.75)
plot(loess, type = "l", xlab = "", ylab = "")

## Savitzky–Golay filter
savitzky <- smooth_savitzky(x, y, m = 21, p = 2)
plot(savitzky, type = "l", xlab = "", ylab = "")

## Whittaker smoothing
whittaker <- smooth_whittaker(x, y, lambda = 1600, d = 2)
plot(whittaker, type = "l", xlab = "", ylab = "")

Whittaker Smoothing

Description

Whittaker Smoothing

Usage

smooth_whittaker(x, y, ...)

## S4 method for signature 'numeric,numeric'
smooth_whittaker(x, y, lambda = 1600, d = 2, sparse = FALSE)

## S4 method for signature 'ANY,missing'
smooth_whittaker(x, lambda = 1600, d = 2, sparse = FALSE)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

lambda

An integer giving the smoothing parameter. The larger lambda is, the smoother the curve.

d

An integer specifying the order of the penalty.

sparse

A logical scalar: should sparse matrices be used for computation? If TRUE, Matrix is required.

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

References

Eilers, P. H. C. (2003). A Perfect Smoother. Analytical Chemistry, 75(14): 3631-36. doi:10.1021/ac034173t.

See Also

Other smoothing methods: smooth_likelihood(), smooth_loess(), smooth_rectangular(), smooth_savitzky(), smooth_triangular()

Examples

## Simulate data with some noise
x <- seq(-4, 4, length = 100)
y <- dnorm(x) + rnorm(100, mean = 0, sd = 0.01)

## Plot spectrum
plot(x, y, type = "l", xlab = "", ylab = "")

## Rectangular smoothing
unweighted <- smooth_rectangular(x, y, m = 3)
plot(unweighted, type = "l", xlab = "", ylab = "")

## Triangular smoothing
weighted <- smooth_triangular(x, y, m = 5)
plot(weighted, type = "l", xlab = "", ylab = "")

## Loess smoothing
loess <- smooth_loess(x, y, span = 0.75)
plot(loess, type = "l", xlab = "", ylab = "")

## Savitzky–Golay filter
savitzky <- smooth_savitzky(x, y, m = 21, p = 2)
plot(savitzky, type = "l", xlab = "", ylab = "")

## Whittaker smoothing
whittaker <- smooth_whittaker(x, y, lambda = 1600, d = 2)
plot(whittaker, type = "l", xlab = "", ylab = "")

Subset

Description

Usage

signal_select(x, y, ...)

signal_slice(x, y, ...)

## S4 method for signature 'numeric,numeric'
signal_select(x, y, from, to)

## S4 method for signature 'ANY,missing'
signal_select(x, from, to)

## S4 method for signature 'numeric,numeric'
signal_slice(x, y, subset)

## S4 method for signature 'ANY,missing'
signal_slice(x, subset)

Arguments

x, y

A numeric vector. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

from, to

A numeric value giving the first and last value (in x unit) to be selected.

subset

An integer vector giving either positive values to keep, or negative values to drop. The values provided must be either all positive or all negative (coerced to integer as by as.integer()).

Value

Returns a list with two components x and y.

Author(s)

N. Frerebeau

See Also

Other signal processing methods: signal_bind(), signal_correct(), signal_drift(), signal_mean(), signal_shift()

Examples

## gamma-ray spectrometry
data("BEGe")

## Plot spectrum
plot(BEGe, type = "l", xlab = "Energy (keV)", ylab = "Count")

## Subset from 2.75 keV to 200 keV
BEGe_1 <- signal_select(BEGe, from = 3, to = 200)

## Plot spectrum
plot(BEGe_1, type = "l", xlab = "Energy (keV)", ylab = "Count")

## Subset from the 20th to the 1250th value
BEGe_2 <- signal_slice(BEGe, subset = 20:1250)

## Plot spectrum
plot(BEGe_2, type = "l", xlab = "Energy (keV)", ylab = "Count")

Sliding Windows

Description

There will be (m1)/2(m - 1) / 2 points both at the beginning and at the end of the data series for which a complete mm-width window cannot be obtained. To prevent data loss, progressively wider/narrower windows are evaluated at both ends of the data series.

Usage

window_sliding(n, m, ...)

## S4 method for signature 'integer,integer'
window_sliding(n, m, i = NULL)

## S4 method for signature 'numeric,numeric'
window_sliding(n, m, i = NULL)

Arguments

n

An integer giving the length of the data series (will be coerced with as.integer() and hence truncated toward zero).

m

An odd integer giving the window size, i.e. the number of adjacent points to be used (will be coerced with as.integer() and hence truncated toward zero).

...

Currently not used.

i

A vector integer specifying the indices of the data points for which windows should be returned. If NULL (the default), windows are evaluated for each data point.

Value

Returns a length-nn list of integer vectors (indices of the data points in each window).

Author(s)

N. Frerebeau

See Also

Other moving windows: window_tumbling()

Examples

## Length of the data series
n <- 10

## Progressive sliding windows
sliding <- window_sliding(n = n, m = 5)

plot(NULL, xlim = c(1, n), ylim = c(1, 10.5), xlab = "Index", ylab = "Window")
for (i in seq_along(sliding)) {
  w <- sliding[[i]]
  text(x = w, y = rep(i, length(w)), labels = w, pos = 3)
  lines(w, rep(i, length(w)), type = "l", lwd = 2)
}

## Tumbling windows
## (compare with drop = TRUE)
tumbling <- window_tumbling(n = n, m = 3, drop = FALSE)

plot(NULL, xlim = c(1, n), ylim = c(1, 5.5), xlab = "Index", ylab = "Window")
for (i in seq_along(tumbling)) {
  w <- tumbling[[i]]
  text(x = w, y = rep(i, length(w)), labels = w, pos = 3)
  lines(w, rep(i, length(w)), type = "l", lwd = 2)
}

Tumbling Windows

Description

Tumbling Windows

Usage

window_tumbling(n, m, ...)

## S4 method for signature 'integer,integer'
window_tumbling(n, m, drop = FALSE)

## S4 method for signature 'numeric,numeric'
window_tumbling(n, m, drop = FALSE)

Arguments

n

An integer giving the length of the data series (will be coerced with as.integer() and hence truncated toward zero).

m

An integer giving the window size, i.e. the number of adjacent points to be used (will be coerced with as.integer() and hence truncated toward zero).

...

Currently not used.

drop

A logical scalar: if m is not a multiple of n, should the last data points be removed so that all windows have the same length?

Value

Returns a list of integer vectors (indices of the data points in each window).

Author(s)

N. Frerebeau

See Also

Other moving windows: window_sliding()

Examples

## Length of the data series
n <- 10

## Progressive sliding windows
sliding <- window_sliding(n = n, m = 5)

plot(NULL, xlim = c(1, n), ylim = c(1, 10.5), xlab = "Index", ylab = "Window")
for (i in seq_along(sliding)) {
  w <- sliding[[i]]
  text(x = w, y = rep(i, length(w)), labels = w, pos = 3)
  lines(w, rep(i, length(w)), type = "l", lwd = 2)
}

## Tumbling windows
## (compare with drop = TRUE)
tumbling <- window_tumbling(n = n, m = 3, drop = FALSE)

plot(NULL, xlim = c(1, n), ylim = c(1, 5.5), xlab = "Index", ylab = "Window")
for (i in seq_along(tumbling)) {
  w <- tumbling[[i]]
  text(x = w, y = rep(i, length(w)), labels = w, pos = 3)
  lines(w, rep(i, length(w)), type = "l", lwd = 2)
}

Powder X-ray Diffraction

Description

Powder X-ray Diffraction

Usage

XRD

Format

A data.frame with 2989 rows and 2 variables.

theta
count

See Also

Other datasets: BEGe, LaBr

Examples

data("XRD")
plot(XRD, type = "l", xlab = expression(2*theta), ylab = "Count")