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.

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.

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.

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.

(a) half-wave

(b) even quarter-wave

(c) odd quarter-wave

(d) odd.

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).

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.

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.

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

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).