helpFunctionsFilter: Convolved piecewise constant signals

Description

Creates piecewise constant signals with a single jump / peak. Computes the convolution of piecewise constant signals with the kernel of a lowpass filter.

Usage

getConvolution(t, stepfun, filter, truncated = TRUE)
getSignalJump(t, cp, leftValue, rightValue)
getConvolutionJump(t, cp, leftValue, rightValue, filter, truncated = TRUE)
getSignalPeak(t, cp1, cp2, value, leftValue, rightValue) 
getConvolutionPeak(t, cp1, cp2, value, leftValue, rightValue, filter, truncated = TRUE)

Arguments

a numeric vector giving the time points at which the signal / convolution should be computed

stepfun

specification of the piecewise constant signal, i.e. a data.frame with named arguments leftEnd, rightEnd and value giving the start and end points of the constant segments and the values on the segments, for instance an object of class stepblock as available by the package 'stepR'

cp, cp1, cp2

a single numeric giving the location of the single, first and second jump point, respectively

value, leftValue, rightValue

a single numeric giving the function value at, before and after the peak / jump, respectively

filter

an object of class lowpassFilter giving the analogue lowpass filter

truncated

a single logical (not NA) indicating whether the signal should be convolved with the truncated or the untruncated filter kernel

Value

a numeric of length length(t) giving the signal / convolution at time points t

References

Pein, F., Bartsch, A., Steinem, C., and Munk, A. (2020) Heterogeneous idealization of ion channel recordings - Open channel noise. Submitted.

Pein, F., Tecuapetla-G<U+00F3>mez, I., Sch<U+00FC>tte, O., Steinem, C., Munk, A. (2018) Fully-automatic multiresolution idealization for filtered ion channel recordings: flickering event detection. IEEE Trans. Nanobioscience, 17(3):300-320.

Pein, F. (2017) Heterogeneous Multiscale Change-Point Inference and its Application to Ion Channel Recordings. PhD thesis, Georg-August-Universit<U+00E4>t G<U+00F6>ttingen. http://hdl.handle.net/11858/00-1735-0000-002E-E34A-7.

Examples

Run this code

# NOT RUN {
# creating and plotting a signal with a single jump at 0 from 0 to 1
time <- seq(-2, 13, 0.01)
signal <- getSignalJump(time, 0, 0, 1)
plot(time, signal, type = "l")

# setting up the filter
filter <- lowpassFilter(param = list(pole = 4, cutoff = 0.1))

# convolution with the truncated filter
convolution <- getConvolutionJump(time, 0, 0, 1, filter)
lines(time, convolution, col = "red")

# without truncating the filter, looks almost equal
convolution <- getConvolutionJump(time, 0, 0, 1, filter, truncated = FALSE)
lines(time, convolution, col = "blue")


# creating and plotting a signal with a single peak with jumps
# at 0 and at 3 from 0 to 1 to 0
time <- seq(-2, 16, 0.01)
signal <- getSignalPeak(time, 0, 3, 1, 0, 0)
plot(time, signal, type = "l")

# convolution with the truncated filter
convolution <- getConvolutionPeak(time, 0, 3, 1, 0, 0, filter)
lines(time, convolution, col = "red")

# without truncating the filter, looks almost equal
convolution <- getConvolutionPeak(time, 0, 3, 1, 0, 0, filter, truncated = FALSE)
lines(time, convolution, col = "blue")


# doing the same with getConvolution
# signal can also be an object of class stepblock instead,
# e.g. constructed by stepR::stepblock
signal <- data.frame(value = c(0, 1, 0), leftEnd = c(-2, 0, 3), rightEnd = c(0, 3, 16))

convolution <- getConvolution(time, signal, filter)
lines(time, convolution, col = "red")

convolution <- getConvolution(time, signal, filter, truncated = FALSE)
lines(time, convolution, col = "blue")


# more complicated signal
time <- seq(-2, 21, 0.01)
signal <- data.frame(value = c(0, 10, 0, 50, 0), leftEnd = c(-2, 0, 3, 6, 8),
                     rightEnd = c(0, 3, 6, 8, 21))

convolution <- getConvolution(time, signal, filter)
plot(time, convolution, col = "red", type = "l")

convolution <- getConvolution(time, signal, filter, truncated = FALSE)
lines(time, convolution, col = "blue")
# }