Fourier Series for Odd
and Even Functions
Even Functions
Definition: A function f(x) is said to be even if f(-x) = f(x).
e.g. x2, cosx are even function
Graphically, an even function is symmetrical about y-axis
Even Functions Cont.
The examples of even functions are:
Even Functions Cont.
When function is even:
When f(x) is an even function then f(x) sinx is an odd
function
Odd Functions
Definition: A function f(x) is said to be even if f(-x)=-f(x).
e.g. sin x, are odd functions.
Graphically, an even function is symmetrical about
the origion.
Odd Functions
When f(x) is an odd function then f(x)cosnx is an odd function and f(x)sinnx is
an even function.
Therefore,
EXAMPLE: EVEN
EXAMPLE: EVEN
EXAMPLE: EVEN
EXAMPLE: EVEN
EXAMPLE: ODD
EXAMPLE: ODD