GATE Electrical Engineering Practice Quiz

Question 1

For $x(t)=2+6$ cos(100πt-π/4), written as $x(t)=Σ_{k=-∞}^{∞} C_k e^{jkω0t}$ with $ω0=100π$ rad/s, what are the nonzero Fourier series coefficients?

Accepted Answer

$C0=2, C1=3e^{-jπ/4}, C-1=3e^{jπ/4}$

Question 2

A 2π-periodic signal is defined as x(t)=1 for -π<t<0 and x(t)=3 for 0<t<π. What value does its Fourier series converge to at t=0?

Accepted Answer

2

Question 3

Let x(t) and y(t) be 2π-periodic signals with CTFS coefficients Ck and Dk respectively, using basis $e^{jkt}$. Define $z(t)=∫_{0}^{2π} x(λ)y(t-λ)dλ$. What is the CTFS coefficient Zk of z(t)?

Accepted Answer

Zk=2πCkDk

Question 4

If x(t) has CTFS coefficients Ck with fundamental frequency ω0, and y(t)=x(t) cos(2ω0t), what is the CTFS coefficient Dk of y(t)?

Accepted Answer

Dk=(Ck-2+Ck+2)/2

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