1
GATE EE 2022
+1
-0.33

The discrete time Fourier series representation of a signal x[n] with period N is written as $$x[n] = \sum\nolimits_{k = 0}^{N - 1} {{a_k}{e^{j(2kn\pi /N)}}}$$. A discrete time periodic signal with period N = 3, has the non-zero Fourier series coefficients : a$$-$$3 = 2 and a4 = 1. The signal is

A
$$2 + 2{e^{ - \left( {j{{2\pi } \over 6}n} \right)}}\cos \left( {{{2\pi } \over 6}n} \right)$$
B
$$1 + 2{e^{\left( {j{{2\pi } \over 6}n} \right)}}\cos \left( {{{2\pi } \over 6}n} \right)$$
C
$$1 + 2{e^{\left( {j{{2\pi } \over 3}n} \right)}}\cos \left( {{{2\pi } \over 6}n} \right)$$
D
$$2 + 2{e^{\left( {j{{2\pi } \over 6}n} \right)}}\cos \left( {{{2\pi } \over 6}n} \right)$$
2
GATE EE 2017 Set 1
Numerical
+1
-0
Consider $$g\left(t\right)=\left\{\begin{array}{l}t-\left\lfloor t\right\rfloor,\\t-\left\lceil t\right\rceil,\end{array}\right.\left.\begin{array}{r}t\geq0\\otherwise\end{array}\right\}$$$where $$t\;\in\;R$$ Here, $$\left\lfloor t\right\rfloor$$ represents the largest integer less than or equal to t and $$\left\lceil t\right\rceil$$ denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing g(t) is _________. Your input ____ 3 GATE EE 2014 Set 1 MCQ (Single Correct Answer) +1 -0.3 For a periodic square wave, which one of the following statements is TRUE? A The Fourier series coefficients do not exist B The Fourier series coefficients exist but the reconstruction converges at no point C The Fourier series coefficients exist and the reconstruction converges at most points. D The Fourier series coefficients exist and the reconstruction converges at every point 4 GATE EE 2011 MCQ (Single Correct Answer) +1 -0.3 The fourier series expansion $$f\left(t\right)\;=\;a_0\;+\;\sum_{n=1}^\infty a_n\cos\;n\omega t\;+\;b_n\sin\;n\omega t$$$ of the periodic signal shown below will contain the following nonzero terms
A
$$a_0\;and\;b_n\;,\;n=1,\;3,\;5,\;..............\infty$$
B
$$a_0\;and\;a_n\;,\;n=1,\;2,\;3,\;..............\infty$$
C
$$a_0\;,\;a_n\;and\;b_n\;,\;n=1,\;2,\;3,\;..............\infty$$
D
$$a_0\;and\;a_n\;,\;n=1,\;3,\;5,\;..............\infty$$
EXAM MAP
Medical
NEET