By Sol Sherr (Eds.)
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Most commonly, this appears as a two-dimensional coordinate system, such as the row and column character position on a display and the (x, y) pair input from a tablet. The method of indicating a point in an TV-dimensional space is as a vector, written x = (xl,x2,. ,*„). 29) Each xt is the length to the point along the fth dimension (or axis). Special vectors are often used to represent a unit distance along one axis. They are denoted with a caret. Any vector can be written as a sum of unit vectors multiplied by a scalar length along that axis.
This method has the advantage that if the empirical fit is performed and stored for each device, variations among devices can be minimized. The device can also be recalibrated during its life to account for aging. From a theoretical point of view, the appropriate method is to approximate the nonlinear function using orthogonal polynomials. 19) 1 /: Lnn, n = m where fn(x) is an orthogonal polynomial or order n evaluated at x, a < x < b, and w(x) is a function called the weighting function. The interval (a, b) over which the orthogonal polynomial is defined and the weighting function are properties of the particular orthogonal polynomials.
However, the counting accuracy must really be considered to be ± ^ count since there is an unknown phase between the measured signal and the reference clock. Since the accuracy is in counts, the fractional error is 1/iV, which is large for small numbers of counts. As an example, consider measuring low frequencies by counting for 1 second. 75 Hz signal is impossible with a single measurement. The converter function in a timing based input system lies in determining when an interval starts or stops, or when an event to count has taken place.