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Fourier series of any periodic signal x(t) can be obtained if

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

2. A finite number of discontinuities within finite time interval t

3. infinite number of discontinuities.

Select the correct answer using the codes given below:

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ESE Electrical 2017 Official Paper
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  1. 1, 2 and 3

  2. 1 and 3 only
  3. 1 and 2
  4. 2 and 3 only

Answer (Detailed Solution Below)

Option 3 : 1 and 2
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Detailed Solution

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Fourier series exist for only periodic signals.

For a signal to have Fourier series, it is necessary to follow “Principle of orthogonality”, It states that the signal x(t) and g(t) are orthogonal if \(\mathop \smallint \limits_{{t_1}}^{{t_2}} x\left( t \right)g\left( t \right) = 0\)

Signal should have finite no. of maxima and minima over its time period.
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