Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

B.3 ORDER NOTATION

Order notation is used to represent the behavior of a function g(x) as .

Definition: Big O Notation Function g(x) is of order h(x) for large x if

(B.23)

for some nonzero . It is written using big O notation as g(x) = O(h(x)).

This means that the two functions change at a similar rate.

Definition: Little O Notation Function g(x) is of order zero relative to h(x) for large x if

(B.24)

It is written using little o notation as g(x) = O(h(x)).

This means that h(x) increases faster than g(x).

Example B.13. For the polynomial g(x) = 2x3+x+1, we can state the following:

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From this simple example, we see that describes the “type” of function. Thus, a constant, a linear ...