Fourier Series- 1 - Free MCQ Practice Test with solutions, GATE EE Signals

Given  C₃ = 3 + 5j
We know that for real periodic signal

So, 
The correct answer is: 3 – 5j

If periodic function is odd the dc term a₀ = 0 and also cosine terms (even symmetry)
It contains only sine terms.
The correct answer is: sine terms

→  x(t) = 2cos t + 3cos t is periodic signal with fundamental frequency ω = 1.
→  The frequency of first term  frequency of 2nd term is ω₂ = 1.
 is not the rational number
 So, x(t) is a periodic or not periodic.
→ x(t) = cos t + 0.5 is a periodic function with
→  first term has frequency 

2nd term has frequency 

So about ratio is rational number x(t) is a periodic signal, with fundamentalfrequency 
Since function in (b) is non periodic. So does not satisfy Dirichlet conditionand cannot be expanded in Fourier series.
The correct answer is: 

 Answer :- c

Solution :- The dc component of x(t) is :

The trigonometric Fourier series of an even function has cosine terms which are even functions.
It has dc term if its average value is finite and no dc term if average value is zero.
So it does not have sine terms.
The correct answer is: Sine terms

→  3sin(25t) is periodic ω = 25.
→ 4cos(20t + 3) + 2sin(710t) sum of two periodic function is also periodic function
→ e sin 25t Due to decaying exponential decaying function it is not periodic.
So Fourier series cannot be defined for it.
→ Constant, Fourier series exists.
Fourier series can’t be defined for option (c).
The correct answer is: exp(–|t|) sin(25t)

The Fourier series for a real periodic function has cosine terms if it is even and sine terms if it is odd.
The correct answer is: P and S

The given impulse train s(t) with strength of each impulse as 1 is a periodic function with period T₀

where 

The correct answer is: 

Concept:

Fourier Transform:

Some properties of fourier transform:

Analysis:

We know that:

Let F(ω) is the Fourier transform of f(t).