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 fun
Key Features:
- Multiple choice format
- Focus on Fourier coefficients and symmetries
- Ideal for learners and educators alike
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
In the case of a periodic function possessing half-wave symmetry, which Fourier coefficient is zero?
An
Bn
Ao
None of these
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
Which of the following periodic function possesses even symmetry?
Cos 3t
Sin t
T cos 50t
(t + t^2 + t^5)
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
12
10
36
5
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
3T
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
A periodic waveform possessing half-wave symmetry has
Even harmonics
Odd harmonics
Sine terms
Cosine terms
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
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