**Directions:** The below item consists of two statements, one labelled as the 'Statement (I)' and the other as 'Statement (II)'. Examine these two statements carefully and select the answers to these items using the codes given below:

**Statement (I):** Dirichlet's conditions restrict the periodic signal x(t), to be represented by Fourier series, to have only finite number of maxima and minima.

**Statement (II):** x(t) should possess only a finite number of discontinuities.

This question was previously asked in

ESE Electronics 2015 Paper 1: Official Paper

Option 2 : Both Statement (I) and Statement (II) are individually true but Statement (II) is NOT the correct explanation of Statement (I)

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

**Statement I:**

**Dirichlet conditions:**

1) The Fourier series is a mathematical tool that allows the representation of any periodic signal as the sum of harmonically related sinusoids.

2) Any periodic signal i.e., one for which x(t) = x(t + T), can be expressed by a Fourier series provided that:

- If it is discontinuous, there are a finite number of discontinuous in the period T
- It has a finite average value over a period T.
- It has a finite number of positive and negative maximum in the period T.

3) When these Dirichlet conditions are satisfied, the Fourier series exist else not from the third point above we can conclude that statement I true.

From the 1) condition we can say that statement II true.