criterion of the maximum deviation
trajectory of the maximum deviation
linear and stepwise approximation
minimum sampling interval of time
theorem of minimality
The basic model of the maximum deviations is considered in the article: sinusoidal trajectory of the maximum deviations (TMD), or sinusoidal law of signal variation between its adjacent samples. Based on TMD, as a mathematical model, it’s accepted the expressions for the minimum time intervals of the sampling signal determination. At TMD studying is assumed that the deviation of the signal must come from two equal, successive signal samples. It’s carrying out the study of the signal sum of a linear form and TMD, which is characterized by unequal values of adjacent samples. Four properties of the sum linear form and TMD are obtained and used to prove the theorem of minimality (by contradiction):
- Unequal values of adjacent samples;
- Equality of time sampling interval and time sampling interval of the signal TMD;
- Unequal values of velocity at times of adjacent sampling signal;
- The excess of the initial velocity of TMD in the signal velocity of a linear form.
It’s formulated and proved the theorem of the minimality of time sampling interval of the signal at sites of stepwise and linear approximation of the signal between its adjacent samples if the samples have the same meaning.