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Determine the fundamental period of the following signals: (i) $x(t)=\cos (\frac \pi3t)+\sin(\frac \pi4t)$ (ii) $x[n] = \cos^2[\dfrac \pi an]$
written 9.2 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 7.0 years ago

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 05

Year : DEC 2014
signals and systems
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written 9.2 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 7.0 years ago

i )

Since $\sin (t) = \cos⁡(t- \dfrac π2) \\ ∴\ sin (\dfrac {πt}4)= \cos⁡(\dfrac {πt}4- \dfrac π2)\\ ∴x(t) = \cos(\dfrac π3 t) + \cos⁡(\dfrac {πt}4- \dfrac π2)$

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$T= \dfrac {T_1}{T_2} = \dfrac 68= \dfrac 34$

Since T it is a rational ∴ signal is periodic

∴ Fundamental period $(T) …

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