GATE EC ||SIGNALS AND SYSTEMS ||FOURIER SERIES & FOURIER TRANSFORM || PYQs

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Question 1

One period (0, T) each of two periodic waveforms W₁ and W₂ are shown in the figure. The magnitudes of the n^th Fourier series coefficients of W₁ and W₂, for n ≥ 1, n is odd, are respectively proportional to

(GATE 2000 || EC || PYQ || MCQ || 2 MARKS)

|n|^–3 and |n|^–2
|n|^–2 and |n|^–3
|n|^–1 and |n|^–2
|n|^–4 and |n|^–2

Question 2

A periodic g(t) is shown in figure. Determine the PSD of g(t).

(GATE 2001 || EC || PYQ || NAT || 5 MARKS)

Question 3

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

(GATE 2001 || EC || PYQ || MCQ || 1 MARKS)

x(t) = 2cost + 3cos3t
x(t) = 2cost + 7cost
x(t) = cost + 0.5
x(t) = 2cos1.5πt + sin 3.5πt

Question 4

The Fourier series expansion of a real periodic signal with fundamental frequency f₀ is given by

it is given that C₃ = 3 + j5. Then C_–3 is

(GATE 2003 || EC || PYQ || MCQ || 1 MARKS)

5 + j3
–3 – j5
–5 + j3
3 – j5

Question 5

Choose the function f(t), –∞< t <∞, for which a Fourier series cannot be defined?

(GATE 2005 || EC || PYQ || MCQ || 1 MARKS)

3sin (25t)
4cos (20t + 3) + 2sin(10t)
exp (–|t|) sin (25t)
1

Question 6

A function is given by f(t) = sin²t + cos 2t. Which of the following is true?

(GATE 2009 || EC || PYQ || MCQ || 1 MARKS)

Question 7

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 statements are correct?

(GATE 2009 || EC || PYQ || MCQ || 1 MARKS)

P and S
P and R
Q and S
Q and S

Question 8

The trigonometric Fourier series for the waveform f(t) shown below contains

(GATE 2010 || EC || PYQ || MCQ || 1 MARKS)

Only cosine terms and zero value for the dc component
Only cosine terms and a positive value for the dc component
Only cosine terms and a negative value for the dc component
Only sine terms and a negative for the dc component

Question 9

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

(GATE 2011 || EC || PYQ || MCQ || 1 MARKS)

dc term
cosine terms
sine terms
odd harmonic terms

Question 10

Consider the periodic square wave in the figure shown.

The ratio of the power in the 7^th harmonic to the power in the 5^th harmonic for this waveform is closest in value to _____.

(GATE 2014 || EC || PYQ || NAT || 1 MARKS)

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