Trigonometric Polynomial - Formal Definition

Formal Definition

Any function T of the form

with an, bn in C for 0 ≤ n ≤ N, is called a complex trigonometric polynomial of degree N (Rudin 1987, p. 88). Using Euler's formula the polynomial can be rewritten as

Analogously let an, bn be in R, 0 ≤ n ≤ N and aN ≠ 0 or bN ≠ 0 then

is called real trigonometric polynomial of degree N (Powell 1981, p. 150).

Read more about this topic:  Trigonometric Polynomial

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