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GATE ECE

Representation of Continuous Time Signal Fourier Series

Signals and Systems

Previous Years Questions

Marks 1

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Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among th...
GATE ECE 2018
Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by 𝑎...
GATE ECE 2018
A periodic signal x(t) has a trigonometric Fourier series expansion $$$x\left(t\right)=a_0\;+\;\sum_{n=1}^\infty\left(a_...
GATE ECE 2017 Set 1
Consider the periodic square wave in the figure shown. The ratio of the power in the 7th harmonic to the power in the 5...
GATE ECE 2014 Set 2
The trigonometric Fourier series for the waveform f(t) shown below contains ...
GATE ECE 2010
A function is given by f(t) = sin2t +cos2t . Which of the following is true?
GATE ECE 2009
The Fourier series of a real periodic function has only P. Cosine terms if it is even Q. Sine terms if it is even R. Cos...
GATE ECE 2009
Choose the function f (t );−$$\infty$$ < 1 < +$$\infty$$, for which a Fourier series cannot be defined.
GATE ECE 2005
Which of the following cannot be the Fourier series expansion of a periodic signal?
GATE ECE 2002
The trigonometric Fourier series of a periodic time function can have only
GATE ECE 1998
The trigonometric Fourier series of an even function of time does not have the
GATE ECE 1996
The Fourier Series of an odd periodic function, contains only
GATE ECE 1994

Marks 2

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Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier ser...
GATE ECE 2017 Set 1
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(...
GATE ECE 2001
Which of the following signals is/are periodic?
GATE ECE 1992

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