GATE ECE

Signals and Systems

Representation of Continuous Time Signal Fourier Series

Previous Years Questions

## Marks 1

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

Let the input be
u
and the output be
y
of a system, and the other parameters are real
constants. Identify which among the following systems is not a l...

A periodic signal x(t) has a trigonometric Fourier series expansion
$$$x\left(t\right)=a_0\;+\;\sum_{n=1}^\infty\left(a_n\cos\;n\omega_0t\;+\;b_n\sin\...

Consider the periodic square wave in the figure shown.
The ratio of the power in the 7th harmonic to the power in the 5th harmonic for this waveform ...

The trigonometric Fourier series for the waveform f(t) shown below contains
...

The Fourier series of a real periodic function has only
P. Cosine terms if it is even
Q. Sine terms if it is even
R. Cosine terms if it odd
S. Sine te...

A function is given by f(t) = sin2t +cos2t . Which of the following is true?

Choose the function f (t );−$$\infty$$ < 1 < +$$\infty$$, for which a Fourier series cannot be
defined.

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

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

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

The Fourier Series of an odd periodic function, contains only

## Marks 2

Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak}
be the complex Fourier series coefficients of x(t), wher...

The PSD and the power of a signal g(t) are, respectively, Sg($$\omega$$) and Pg. The PSD
and the power of the signal ag(t) are, respectively...

Which of the following signals is/are periodic?