Find averaged xy plots

If there are multiple 2D plots where the range of the x values are the same, then this function can allow you to average the y-values for all of these plots. The increment of the x-values can be different because this function uses interpolation to ensure each window has the same x-axis when the averaging step occurs.

MakeCompositeXYPlotForAllWindows(
  list.of.windows,
  name.of.col.containing.time.series,
  x_start = 0,
  x_end,
  x_increment
)

Arguments

list.of.windows

A list of windows (dataframes). Each window should have the same range of values in the x-axis in order for averaging to work.
name.of.col.containing.time.series

A string that specifies the name of the column in the windows that correspond to the time series that should be used for making averaging.
x_start

Numeric value specifying start of the new x-axis for the averaged PSD. Default is 0, so the first observation in the time series corresponds with x = 0.
x_end

Numeric value specifying end of the new x-axis for the averaged PSD. Maximum value is the sampling_frequency divided by 2.
x_increment

Numeric value specifying increment of the new x-axis for the averaged PSD.

Value

  1. Vector of x values for plotting. The units will be number of observations. So if the time series has 100 observations and x_increment used is 1, then each tick mark on the x-axis corresponds to one observation unit.

  2. Vector of averaged y values after looking at all windows.

  3. Vector of standard deviation of y values for each x value.

Examples

#Create a vector of time that represent times where data are sampled.
Fs = 100; #sampling frequency in Hz
T = 1/Fs; #sampling period
L = 1000; #length of time vector
t = (0:(L-1))*T; #time vector

#First signal
#1. 1 Hz with amplitude of 4
S1 <- 4*sin(2*pi*1*t)
S1.data.frame <- as.data.frame(cbind(t, S1))
colnames(S1.data.frame) <- c("Time", "Signal")

#Second signal
#1. 1 Hz with amplitude of -2
#2. 2 Hz with amplitude of -2
S2 <- (-2)*sin(2*pi*1*t) - 2*sin(2*pi*2*t);
S2.data.frame <- as.data.frame(cbind(t, S2))
colnames(S2.data.frame) <- c("Time", "Signal")

#Third signal
#1. 1 Hz with amplitude of 2
#2. 2 Hz with amplitude of 2
S3 <- 2*sin(2*pi*1*t) + 2*sin(2*pi*2*t);
S3.data.frame <- as.data.frame(cbind(t, S3))
colnames(S3.data.frame) <- c("Time", "Signal")

#Add all signals to a List
list.of.windows <- list(S1.data.frame, S2.data.frame, S3.data.frame)

results <- MakeCompositeXYPlotForAllWindows(list.of.windows, "Signal", 0, 999, 1)

x.values <- results[[1]]

y.values <- results[[2]]

stddev.y.values <- results[[3]]

#plot each xy plot individually
#dev.new()
plot(t, S1, ylim = c(-5, 5), type = "l")

lines(t, S2, col="blue")

lines(t, S3, col="green")



#plot the averaged plot
#The only curve remaining should be the 1Hz with amplitude of 4/3.
#dev.new()
plot(x.values, y.values, type = "l")


#plot averaged plot with error bars
#dev.new()
plot(x.values, y.values, type = "l")

#Add error bars
arrows(x.values, y.values, x.values, y.values + stddev.y.values, length=0.05, angle=90)

#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
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#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
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arrows(x.values, y.values, x.values, y.values - stddev.y.values, length=0.05, angle=90)

#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
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#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped
#> Warning: zero-length arrow is of indeterminate angle and so skipped