Test: Fourier Series- 1
10 Questions MCQ Test Signals and Systems | Test: Fourier Series- 1
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The Fourier series expansion of a real periodic signal with fundamental frequency f0 is given by
It is given that C3 = 3 + 5j then C-3 is
Select one:
It is given that C3 = 3 + 5j then C-3 is
Select one:
Given C3 = 3 + 5j
We know that for real periodic signal
So, 
The correct answer is: 3 – 5j
The Fourier series of an odd periodic function, contains only
Select one:
Select one:
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
The trigonometric Fourier series of an even function of time does not have
Select one:
Select one:
For periodic even function, the trigonometric Fourier series does not contain the sine terms (odd functions.)
It has dc term and cosine terms of all harmonic.
The correct answer is: Sine terms
Trigonometric Fourier series of a periodic time function can have only
Select one:
Which of the following cannot be the Fourier series expansion of a periodic signals?
Select one:
→ 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: 
A periodic signal x(t) of period T0 is given by
The dc component of x(t) is
Select one:
Answer :- c
Solution :- The dc component of x(t) is :
The trigonometric Fourier series of an even function does not have the
Select one:
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
Choose the function 
for which a Fourier series cannot be defined
Select one:
→ 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 of a real periodic function has only
P. Cosine terms if it is even
Q. Sine terms if it is even
R. Cosine terms if it is odd
S. Sine terms if it is odd
Which of the above statement is correct?
Select one:
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 Fourier series representation of an impulse train denoted by
Select one:
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: 
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