Waveform Comparison

This analysis can display:

• Means and standard deviations of the waveform variables in specified time intervals

• Waveforms in the Principal Component space

• Trough and peak values and other features of the waveforms

Parameters

Parameter	Description
Select Data	If Select Data is From Time Range, only the data from the specified (by Select Data From and Select Data To parameters) time range will be used in analysis. See also Data Selection Options.
Select Data From	Start of the time range in seconds.
Select Data To	End of the time range in seconds.
Interval filter	Specifies the interval filter(s) that will be used to preselect data before analysis. See also Data Selection Options.
What to Draw	Specifies graphics output (means and standard deviations of waveforms, projections in the Principal Component space or trough and peak values).
Draw Variation	An option to draw waveform variation as a colored background (means and standard deviations display).
Variation (standard deviations)	Number of standard deviations in the colored background around waveform mean (means and standard deviations display).
Variation Background Color	The color to be used for drawing of the colored background around waveform mean (means and standard deviations display).
PC X Axis	Which principal component to use for X axis for the Principal Component projections display.
PC Y Axis	Which principal component to use for Y axis for the Principal Component projections display.
Trough/peak X Axis	Which waveform feature to use for X axis for the trough and peak display.
Trough/peak Y Axis	Which waveform feature to use for Y axis for the trough and peak display.
Peak calculation	Use the first local maximum after trough or use maximum with the highest value after trough.
Width at half height baseline	Use the last local maximum before trough as the baseline or use zero as the baseline.

Summary of Numerical Results

The following information is available in the Summary of Numerical Results

Column	Description
Variable	Variable name.
YMin	Y Axis minimum.
YMax	Y Axis maximum.
Filter Length	The length of all the intervals of the interval filter (if a filter was used) or the length or the recording session (in seconds)
Mean Waveform Min	Minimum of the mean waveform.
Mean Waveform Max	Maximum of the mean waveform.
ProjPc1	Principal component display only. Projection to principal component 1.
ProjPc2	Principal component display only. Projection to principal component 2.
ProjPc3	Principal component display only. Projection to principal component 3.
ProjPc4	Principal component display only. Projection to principal component 4.
TroughTime	Trough/peak display only. Trough time in milliseconds.
TroughValue	Trough/peak display only. Trough value in milliVolts.
PeakTime	Trough/peak display only. Peak time in milliseconds.
PeakValue	Trough/peak display only. Peak value in milliVolts.
TroughToPeakDuration	Trough/peak display only. Distance in time from trough to peak (milliseconds).
WidthAtHalfHeight	Trough/peak display only. Width of the trough at half height (milliseconds).
TroughToPeakSlope	Trough/peak display only. Angle of the line from trough to peak (degrees).

Algorithm

The program selects waveforms in the specified time range and the interval filter(s) and calculates the mean and the standard deviation of the selected waveforms.

Principal components are calculated from all the waveforms of the given waveform variable.

First, the matrix of covariances between waveform points (c[t, s]) is calculated:

c[t, s] = covariance between vectors waveform_value[t, *] and waveform_value[s,*], s, t = 1, ...,number_of_points_in_each_waveform.

Then, the eigenvalues and eigenvectors are calculated for the matrix c[t, s]. The eigenvectors (principal components) are sorted according to their eigenvalues. The first principal component has the largest eigenvalue.

PCA projection display shows scatter plots where x and y are projections of a waveform to the specified principal components (projection is a sum of products waveform_value[t]*principal_component_value[t]).

Trough and Peak display

The algorithm assumes that the threshold crossing down was used to detect waveforms.

Therefore, the algorithm expects that there is a trough in the waveform followed by a peak:

The algorithm for calculating trough and peak is the following:

1. Each wave is resampled at 1 microsecond resolution using cubic splines.

2. The local minima of the resampled waveform are found. The local minimum is the waveform point w[i] such that w[i]<w[i-1] and w[i]<w[i+1].

3. The minimum with the smallest voltage value is the trough.

4. Starting with the trough waveform point, the local maxima of the resampled waveform are found.

5. The maximum with the highest voltage value is the peak.

6. The width at half height is a width of the trough negative going dip when the waveform voltage values are equal to voltage_at_trough/2 (blue arrow).