Let  be a periodic signal with fundamental period . Consider the signal , where .

The Fourier series expansions of  and  are given by

Which of the following statements is/are TRUE?

Consider a discrete-time periodic signal with period . Let the discrete-time Fourier series (DTFS) representation be , where

 and . The value of the sum  is

The exponential Fourier series representation of a continuous-time periodic signal  is defined as

where  is the fundamental angular frequency of  and the coefficients of the series are  The following information is given about  and

I.  is real and even, having a fundamental period of 6.

II. The average value of  is 2.

III.

The average power of the signal  (rounded off to one decimal place) is ________.

Let x(t) be a periodic function with period T =10. The Fourier series coefficients for this series are denoted by , that is

The same function x(t) can also be considered as a periodic function with period . Let  be the Fourier series coefficients when period is taken as. If, then,  is equal to

A periodic signal x (t) has a trigonometric Fourier series expansion

, we can conclude that

Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let  be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):

I. The complex Fourier series coefficients of x(3t) are  where k is integer valued

II. The complex Fourier series coefficients of x(3t) are  where k is integer valued

III. The fundamental angular frequency of x(3t) is

For the three statements above, which one of the following is correct?

Consider an LTI system with magnitude response  .          

And phase response  

If the input to the system is

then the average power of the output signal y (t) is ______________

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor(C) elements, connected all in series or all in parallel, is excited with a source of the form where

The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?

A signal is the input to an LTI system with the transfer function

 .. If denotes the  coefficient in the exponential Fourier series of the output signal, then  is equal to

The magnitude and phase of the complex Fourier series coefficients  of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex numbers, R is the set of purely real numbers, and P is the set of purely imaginary numbers         

Letbe a periodic signal with period 16. Its DFS coefficients are defined by for all k . The value of the coefficient  is ____________.

Consider a discrete time periodic signal  . Let  be the complex Fourier series coefficients of x[n]. The coefficients {} are non-zero when, where m is any integer. The value of B is _____________.

Consider the periodic square wave in the figure shown.

The ratio of the power in the  harmonic to the power in the  harmonic for this waveform is closest in value to _______.

The trigonometric Fourier series of an even function of time does not have the

The Fourier series expansion of a real periodic signal with fundamental frequency  is given by  it is given that. Then  is

Which of the following cannot be the Fourier series expansion of a periodic signal?

One period (0, T) each of two periodic waveforms,  and  are shown in figures. The magnitudes of the  Fourier series coefficients of  and , for , n odd, are respectively proportional to

The Fourier series representation of an impulses train denoted by

 is given by        

The trigonometric Fourier series of a periodic time function can have only

A periodic signal x (t) of period  is given by .

The d. c. component of x(t) is

The trigonometric Fourier series of an even function of time does not have the

The Fourier Series of an odd periodic function, contains only