Test: Fourier Series- 2 - Electrical Engineering (EE) MCQ

# Test: Fourier Series- 2 - Electrical Engineering (EE) MCQ

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## 10 Questions MCQ Test Signals and Systems - Test: Fourier Series- 2

Test: Fourier Series- 2 for Electrical Engineering (EE) 2024 is part of Signals and Systems preparation. The Test: Fourier Series- 2 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Fourier Series- 2 MCQs are made for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Fourier Series- 2 below.
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Test: Fourier Series- 2 - Question 1

### Value of bn for the periodic function f with period 2π defined as follows : Select one:

Detailed Solution for Test: Fourier Series- 2 - Question 1

The function is bounded, integrable and piece wise monotonic on
Let us determine the Fourier coefficients

The correct answer is: - 1/n, for n even

Test: Fourier Series- 2 - Question 2

### For the given periodic function  The coefficient b1 of the continuous Fourier series associated with the given function f(t) can be computed as Select one:

Detailed Solution for Test: Fourier Series- 2 - Question 2

The coefficient b1 of the continuous Fourier series associated with the above given function f(t) can be computed as

since  and
Hence

b1 = –0.7468

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Test: Fourier Series- 2 - Question 3

### Given the following periodic function, f(t). f (t) = { t2   for 0 ≤ t ≤ 2  ;    -t + 6   for 2 ≤ t ≤ 6 The coefficient a0 of the continuous Fourier series associated with the above given function f(t) can be computed as Select one:

Detailed Solution for Test: Fourier Series- 2 - Question 3

The coefficient a0 of the continuous Fourier series associated with the given function f(t) can be computed as

Test: Fourier Series- 2 - Question 4

For the given periodic function  with a period T = 6. The Fourier coefficient a1 can be computed as
Select one:

Detailed Solution for Test: Fourier Series- 2 - Question 4

The coefficient a1 of the continuous Fourier series associated with the above given function f(t) can be computed with k = 1 and T = 6 as following :

a1 = –0.9119

Test: Fourier Series- 2 - Question 5

Sum of the series at  for the periodic function f with period 2π is defined as

Select one:

Detailed Solution for Test: Fourier Series- 2 - Question 5

The function is piece wise monotonic, bounded and integrable on [-π, π]  Let us compute its Fourier coefficients

The function is continuous at all points of [-π, π] except

which holds at all points with the exception of all discontinuities,

At  the sum of the series

Test: Fourier Series- 2 - Question 6

Which of the following is an “even” function of t?
Select one:

Detailed Solution for Test: Fourier Series- 2 - Question 6

Since if we replace “t” by “–t”, then the function value remains the same!

Test: Fourier Series- 2 - Question 7

A “periodic function” is given by a function which
Select one:

Detailed Solution for Test: Fourier Series- 2 - Question 7

Since the function’s value remains the same value after a period (or multiple periods) has passed!
The correct answer is: satisfies f(t + T) = f(t)

Test: Fourier Series- 2 - Question 8

For the given periodic function  with a period T = 6. The complex form of the Fourier series can be expressed as   The complex coefficient  can be expressed as
Select one:

Detailed Solution for Test: Fourier Series- 2 - Question 8

The coefficient  (corresponding to k = 1) can be expressed  as :

The coefficient b1 of the continuous Fourier series associated with the above given function f(t) can be computed as

since
and
Hence

b1 = –0.7468
The coefficient a1 of the continuous Fourier series associated with the above given function f(t) can be computed with k = 1 and T = 6 as following :

a1 = –0.9119

The correct answer is: –0.4560 + 0.3734i

Test: Fourier Series- 2 - Question 9

The function x2 is periodic with period 2l on the interval [–l, l]. The value of an is given by
Select one:

Detailed Solution for Test: Fourier Series- 2 - Question 9

The substitution transforms the function into a periodic function with period . Moreover it is an even function.
∴ bn = 0, n = 1, 2, 3,.....

The correct answer is:  for n even

Test: Fourier Series- 2 - Question 10

The function x2 extended as an odd function in [–l, l] by redefining it as

sum of series at x = l.
Select one:

Detailed Solution for Test: Fourier Series- 2 - Question 10

Substitution of  transforms it into an odd periodic function on [-π, π],
so that the Fourier coefficients are
an = 0 for n = 0, 1, 2, 3

At x = 0, a point of continuity of the function, the sum of the series is zero, a fact which may be verified directly from series.
At x = l, the sum of series =

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