Question

Fourier series of any periodic signal x(t) can be obtained if
1. ${\int }_0^T|x\left(t\right)|dt<\infty$
2. Finite number of discontinuities within finite interal t
3. Infinite number of discontinuities

Select the correct answer using the codes below.

• A. 1,2 and 3
• B. 1 and 3 only
• C. 1 and 2 only
• D. 2 and 3 only

Answer 1

The correct option is C

1 and 2 only

Condition for Existence of Fourier series
Condition (1). x(t) must be absolutely integrable over one time period.
${\int }_0^T|x\left(t\right)|dt<\infty$
Condition (2). x(t) has finite number of maxima and minima over one time period.
Condition (3). x(t) has finite number of discontinuity over one time period.