The discrete time Fourier series representation of a signal x[n] with period N is written as . A discrete time periodic signal with period N = 3, has the non-zero Fourier series coefficients:  and . The signal is

Which of the following is true for all possible non-zero choices of integers m, n; m ≠ n, or all possible non-zero choices of real numbers p, q; p ≠ q as applicable?

A periodic function f(t), with a period of , is represented as its Fourier series,        

.

If

,

The Fourier series coefficients  and of f(t) are

Consider

.

Here,  represents the largest integer less than or equal to t and  denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing  is ___________          

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

The signum function is given by

The Fourier series expansion of sgn  has

For a periodic square wave, which one of the following statements is TRUE?

A 10 kHz even-symmetric square wave is passed through a band-pass filter with center frequency at 30 kHz and 3dB pass-band of 6 kHz. The filter output is

For a periodic signal

, the fundamental frequency in rad/s is

The Fourier series expansion of the periodic signal shown below will contain the following nonzero terms                

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

The Fourier Series coefficients, of a periodic signal x(t), expressed as are given by ; ;  ;  ; ; and for  .  Which of the following is true?

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

A signal x(t) is given by         

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

x(t) is a real valued function of a real variable with period T.  Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k)/T; k = 1, 2,……  Also, no sine terms are present.  Then x(t) satisfies the equation

The Fourier series for the function  is:

Fourier Series for the waveform, f(t) shown in Figure is         

Consider the voltage waveform v, shown in figure.

If an ac voltage wave is corrupted with an arbitrary number of harmonics, then the overall voltage waveform differs from its fundamental frequency component in terms of

Compute the amplitude of the fundamental component of the waveform given in figure

A periodic rectangular signal, x(t) has the wave form shown in figure. Frequency of the fifth harmonic of its spectrum is