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Linear mapping maps a curve, which is defined point for point by an x-channel and a y-channel, onto a further x-channel, which is the interpolation channel. For example, linear mapping can convert several signals acquired with different sampling rates onto a joint x-channel. This process is also called down-sampling or up-sampling. Linear mapping offers different mapping modes for analog curves, spike curves, stair curves, and stair/analog curves.
Linear mapping maps the new interpolation points in the joint area of the x-channel and the interpolation channel for the different mapping modes according to the following rules, whereby the original x-values are xi and original y-values are yi = f(xi).
The analog mapping mode creates interim values by interpolating linearly according to the following formula:
The spike mapping mode assigns the spikes to the nearest interpolation points of the new x-channel and sets the other values to zero:
The stair mapping mode continues the function values for the increasing x-values after every slope on a constant level, so that the level is maintained and the value does not return to zero as is the case in spike curves.
The stair/analog mapping mode maintains the low level at least up to the original x-value, unlike normal stair curves.
If the original y-channel contains NoValues, linear mapping can replace these NoValues. For the Analog mapping mode, linear mapping executes a linear interpolation. For the Spike mapping mode, linear mapping replaces the NoValues with zeros. For the Stair mapping mode, linear mapping replaces the NoValues with the last level value. If the Novalues are not to be replaced, linear mapping adopts the NoValues in the new y-channel.
For the digital mapping modes Spike and Stair, the maximum step width of the new interpolation channel must be smaller than half the minimum step width of the original x-channel because otherwise spikes or level changes might be lost. If the step width of the interpolation channel is too large, DIAdem might assign two values y(xa) and y(xb) to the same interpolation value x1. If this is the case, DIAdem adopts the y-value, whose x-value is closer to the new interpolation point x1. If both curve points have the same distance, DIAdem adopts the y-value of the smaller x-value.
If the interpolation channel contains x-values outside the x-range of the existing curve, linear mapping can extrapolate the curve on the extended x-range. If analog curves exceed the original x-area, they are continued either by a freely selected numeric value, by the two y-values of the boundary values, or by a line with the slope at the respective boundary values. Spike functions and stair functions are continued with the value zero or a freely selected numeric value.