Fourier Series

Explore the World of Fourier Series

Test your knowledge on Fourier series and its various properties with this engaging quiz. Whether you're a student, teacher, or just a curious learner, dive into the principles of periodic functions and harmonic analysis. Each question is designed to challenge and enhance your understanding of this fundamental concept in mathematics and engineering.

Key Features:

Multiple choice format
Focus on Fourier coefficients and symmetries
Ideal for learners and educators alike

16 Questions4 MinutesCreated by AnalyzingWaveform512

A given function f(t) can be represented by a Fourier series if it

Is periodic

Is single valued

Has a finite number of maxima and minima in any one period

All of these

In a Fourier series expansion of a periodic function, the coefficient ao represents its

Net area per cycle

D.c. value

Average value over half cycle

Average a.c value per cycle

If in the Fourier series of a periodic function, the coefficient ao is zero, il means that the function has

Odd symmetry

Even quarter-wave symmetry

Odd quarter-wave symmetry

Any of these

A periodic function f (t) is said to possess odd quarter-wave symmetry if

A. f(t) = f(-t)

B. f(-t) = -f(t)

C. f(t) = -f(t + T/2)

D. both B and C

If the average value of a periodic function over one period is zero and it consists of only odd harmonics then it must be possessing symmetry.

Half-wave

Even quarter-wave

Odd quarter-wave

Odd

If in the Fourier series of a periodic function, the coefficient a - 0 and a, - 0, then it must be having symmetry.

A. odd

B. Odd quarter-wave

C. even

D. either A or B

A periodic function has zero average value over a cycle and its Fourier series consists of only odd cosine terms. What is the symmetry possessed by this function.

Even

Odd

Even quarter-wave

Odd quarter-wave

If the Fourier coefficient bn of a periodic function is zero, then it must possess symmetry.

A. even

B. Even quarter-wave

C. odd

Either A or B

A complex voltage waveform is given by V = 120 sin at + 36 sin (3wt + n/2) + 12 sin (5wt + n). It has a time period of T seconds. The percentage fifth harmonic contents in the waveform is

In the waveform given by V = 120 sin at + 36 sin (3wt + n/2) + 12 sin (5wt + n). , the phase displacement of the third harmonic represents a time interval of seconds.

T/12

T/3

T/36

When the negative half-cycle of a complex waveform is reversed, it becomes identical to its positive half-cycle. This feature indicates that the complex waveform is composed of

A. fundamental

B. Odd harmonics

C. Even harmonics

Both A and B

The Fourier series of a wave form possessing even quarter-wave symmetry has only

A. Even harmonics

B. Odd cosine terms

C. Odd sine terms

Both B and C

The Fourier series of a waveform possessing odd quarter-wave symmetry contains only

Even harmonics

Odd cosine terms

Odd sine terms

None of these

Fourier Series

Explore the World of Fourier Series

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