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Consider the following statements:

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

1. 

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

Which of the above statements is/are correct ?

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  1. 1 only
  2. 2 only
  3. Both 1 and 2
  4. Neither 1 nor 2

Answer (Detailed Solution Below)

Option 2 : 2 only
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Detailed Solution

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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,

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.

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