PX153 - J4 - periodic extensions

periodic extension

can be evaluated for any value of $x$ .
a fourier series evaluated in the interval, $[- π, π]$ , will not represent the function outside the interval
the region outside the interval is called the periodic extension
fourier series is periodic:

f (x + 2 π) = f (x) = \frac{a_{0}}{2} + \sum_{n = 1}^{\infty} (a_{n} \cos (n x) + b_{n} \sin (n x))