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Signals and Systems
Fourier Series

Practice questions from Fourier Series.

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Q#1 Fourier Series GATE EC 2025 (Set 1) MSQ +2 marks -0 marks

Let  be a periodic signal with fundamental period . Consider the signal , where .

The Fourier series expansions of  and  are given by

 

Which of the following statements is/are TRUE?

 for all

 is periodic with a fundamental period

 for all

 is periodic with a fundamental period

Explanation:

 

 

 

where,  is fundamental Time period of  

and  is, fundamental Time period of .

Also,

 

Since, .

Thus,  for all

& y(t) is periodic with fundamental period

Hence, option (a) & (d) are correct

Q#2 Fourier Series GATE EC 2023 (Set 1) MCQ +2 marks -0.66 marks

Consider a discrete-time periodic signal with period . Let the discrete-time Fourier series (DTFS) representation be , where

 and . The value of the sum  is

-10

10

-2

2

Explanation:

Let,

 

   …(i)

As we know,

 

Put

Put

From equation (i),