Questions & Answers of Fourier Series Representation of Continuous Periodic Signals

Question No. 120

Let f(x) be a real, periodic function satisfying f-x=-fx. The general form of its Fourier series representation would be

Question No. 38

The signum function is given by

sgnx=xx;x00; x=0

The Fourier series expansion of sgn(cos(t)) has

Question No. 36

Let g:[0,):[0,) be a function defined by gx=x-x, where x represents the integer part of x. (That is, it is the largest integer which is less than or equal to x). The value of the constant term in the Fourier series expansion of gx is _______

Question No. 4

The fourier series expansion $\style{font-size:18px}{f\left(t\right)=a_0+\sum\limits_{n=1}^\infty a_n\cos n\omega t+b_n\sin n\omega t}$ of the periodic signal shown below will contain the following nonzero terms

Question No. 6

The second harmonic component of the periodic waveform given in the figure has an amplitude of

Question No. 36

The Fourier Series coefficient, of a periodic signal x(t), expressed as $\style{font-size:18px}{x\left(t\right)={\textstyle\sum\limits_{k=-\infty}^\infty}a_ke^{\mathrm j2\mathrm{pkt}/\mathrm T}}$ are given by a-2 = 2 - j1; a-1 = 0.5 + j0.2; a0 = j2; a1 = 0.5 + j0.2; a2 = 2 + j1; and ak=0;for k>2. Which of the following is true?

Question No. 31

Let x(t) be a periodic signal with time period T,Let y(t)=x(t-t0)+x(t+t0) for some t0.The Fourier Series coefficients of y(t) are denoted by bk. if bk=0 for all odd k,then t0 can be equal to

Question No. 37

A signal x(t) is given by xt=1,-T/4<t3T/4-1,3T/4<t7T/4-xt+T

Which among the following gives the fundamental Fourier term of x(t)?