Consider the following statements:

Fourier series of any periodic function X(t) can be obtained if

1. \(\mathop \smallint \limits_0^1 \left| {x\left( t \right)} \right|dt < \infty \)

2. Finite number of discontinous exist within finite time interval t.

Which of the above statements is/are correct ?

The convergence of the Fourier series:

It is known that a periodic signal x(t) has a Fourier series representation if it satisfies the following Dirichlet conditions:

x(t) is absolutely integrable over any period, that is,

\(\mathop \smallint \nolimits_{{T_0}} \left| {x\left( t \right)} \right|dt < \infty \)

x(t) has a finite number of maxima and minima within any finite interval of t.

x(t) has a finite number of discontinuities within any finite interval of t, and each of these discontinuities is finite.