HP VXI 75000 C Series, User'S And Scpi Programming Manual

Page: 368 / 438

368 Generating User Defined Functions Appendix F
function over the entire range would severely impact the accuracy of the
approximation. Remember, the entire range is broken up into only 128
segments of Mx+B operations. If you want accuracy, you MUST limit the
range over which calculations are made. Many transcendental functions are
simply used as a scaling multiplier. For example, a sine wave function is
typically created over a range of 360 degrees or 2*PI radians. After which,
the function repeats itself. It’s a simple matter to make sure the ’x’ term is
scaled to this range before calculating the result. This concept should be
used almost exclusively to obtain the best results.
Haversine Example.
The following is an example of creating a haversine function (a sine wave
over the range of -PI/2 to PI/2). The resulting function represents a fairly
accurate approximation of this non-linear waveform when you limit the
range as indicated. Since the tables must be built upon binary
boundaries(i.e. .125, .25, .5, 1, 2, 4, etc.) and since PI/2 is a number greater
than 1 but less than 2, the next binary interval to include this range will be
2. Another requirement for building the table is that the waveform range
MUST be centered around 0( i.e. symmetrical about the X-axis). If the
desired function is not defined on one side or the other of the Y-axis, then
the table is right or left shifted by the offset from X=0 and the table values
are calculated correctly, but the table is built as though it were centered
about the X-axis. For the most part, you can ignore these last couple of
sentences if it does not make sense to you. The only reason its brought up
here is that your accuracy may suffer the farther away from the X=0 point
you get unless you understand what resolution is available and how much
non-linearity is present in your waveform. We’ll talk about that in the
"Limitations" section, later.
Figure 1 shows the haversine function as stated above. This type of
waveform is typical of the kind of acceleration and deceleration one wants
when moving an object from one point to another. The desired beginning
point would be the location at -PI/2 and the ending point would be at PI/2.
With the desired range spread over +/- PI/2, the 128 segments are actually
divided over the range of +/- 2. Therefore, the 128 Mx+B line segments are
divided equally on both sides of X=0: 64 segments for 0..2 and 64 segments
for -2..0.