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QUESTION: 1

The Fourier series expansion of a real periodic signal with fundamental frequency f_{0} is given by

It is given that C_{3} = 3 + 5j then C_{-3} is

Select one:

Solution:

Given C_{3} = 3 + 5j

We know that for real periodic signal

So,

The correct answer is: 3 – 5j

QUESTION: 2

The Fourier series of an odd periodic function, contains only

Select one:

Solution:

If periodic function is odd the dc term a_{0} = 0 and also cosine terms (even symmetry)

It contains only sine terms.

The correct answer is: sine terms

QUESTION: 3

The trigonometric Fourier series of an even function of time does not have

Select one:

Solution:

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

QUESTION: 4

Trigonometric Fourier series of a periodic time function can have only

Select one:

Solution:

QUESTION: 5

Which of the following cannot be the Fourier series expansion of a periodic signals?

Select one:

Solution:

→ x(t) = 2cos t + 3cos t is periodic signal with fundamental frequency ω = 1.

→ The frequency of first term frequency of 2nd term is ω_{2} = 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:

QUESTION: 6

A periodic signal x(t) of period T_{0} is given by

The dc component of x(t) is

Select one:

Solution:

** Answer :- c**

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

QUESTION: 7

The trigonometric Fourier series of an even function does not have the

Select one:

Solution:

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

QUESTION: 8

Choose the function for which a Fourier series cannot be defined

Select one:

Solution:

→ 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)

QUESTION: 9

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:

Solution:

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

QUESTION: 10

The Fourier series representation of an impulse train denoted by

Select one:

Solution:

The given impulse train s(t) with strength of each impulse as 1 is a periodic function with period T_{0
}

where

The correct answer is:

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