Fourier Series Quiz

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

(a) is periodic

(b) is single valued

(c) has a finite number of maxima and minima in any one period

(d) all of the above.

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In a Fourier series expansion of a periodic function, the coefficient a0 represents its

(a) net area per cycle

(b) d.c value

(c) average value over half cycle

(d) average a.c value per cycle.

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If in the Fourier series of a periodic function, the coefficient a0 is zero, it means that the function has

(a) odd symmetry

(b) even quarter-wave symmetry

(c) odd quarter-wave symmetry

(d) any of the above.

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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).

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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.

(a) half-wave

(b) even quarter-wave

(c) odd quarter-wave

(d) odd.

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If in the Fourier series of a periodic function, the coefficient a0 = 0 and an = 0, then it must be having _______ symmetry. (a) odd (b) odd quarter-wave (c) even (d) either (a) or (b).

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In the case of a periodic function possessing half-wave symmetry, which Fourier coefficient is zero ? (a) an (b) bn (c) a0 (d) none of above.

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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. (a) even (b) odd (c) even quarter-wave (d) odd quarter-wave.

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Which of the following periodic function possesses even symmetry ? (a) cos 3t (b) sin t (c) t . cos 50 t (d) (t + t2 + t5).

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If the Fourier coefficient bn of a periodic function is zero, then it must possess ______ symmetry. (a) even (b) even quarter-wave (c) odd (d) either (a) and (b).

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