The energy of the signal x-n-sin2n- n is

By Parsevals theorem, Energy of a signal x[n] is, E=12π∫_ π^π | X(e^jω)^2 |dω where X(e^jω) is discrete time Fourier transform of x[n] So, sin(2n)π nDTFT⟷ X( ...

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Standard XII

Physics

Kinetic Energy Formulae

The energy of...

Question

$The energy of the signal x[n]$ $= \frac{s i n (2 n)}{π n}$ is

0.75 J

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1.24 J

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0.84 J

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0.64 J

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Solution

The correct option is D $0.64 J$
$By Parsevals theorem, Energy of a signal x[n] is, E = \frac{1}{2 π} \int_{- π}^{π} ∣ ∣ X (e^{j ω})^{2} ∣ ∣ d ω where X (e^{j ω}) is discrete time Fourier transform of x[n] So, \frac{s i n (2 n)}{π n} D T F T ⟷ X (e^{j ω}) = {\begin{matrix} 1; & | ω | \leq 2 0; & otherwise \end{matrix} ∴ Energy, E = \frac{1}{2 π} \int_{- 2}^{2} 1 d ω = \frac{1}{2 π} [4] ∴ E = \frac{2}{π} = 0.64 J$

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The energy of the signal x[n]=sin(2n)πn is

The correct option is D 0.64JBy Parsevals theorem,Energy of a signal x[n] is, E=12π∫π−π∣∣X(ejω)2∣∣dωwhereX(ejω)is discrete time Fourier transform of x[n]So,sin(2n)πnDTFT⟷X(ejω)={1;|ω|≤20;otherwise∴Energy, E=12π∫2−21dω=12π[4]∴E=2π=0.64J

$The energy of the signal x[n]$ $= \frac{s i n (2 n)}{π n}$ is