Consider a rectified sine wave x(t) defined by x(t) = |A sin πt|. Determine its fundamental period and complex exponential Fourier series

\({T_0} = \frac{1}{2}\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} + 1}}{e^{jk2\pi t}}\)

\({T_0} = 1\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} - 1}}{e^{jk2\pi t}}\)

\({T_0} = 1\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} + 1}}{e^{jk2\pi t}}\)

\({T_0} = \frac{1}{2}\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} - 1}}{e^{jk2\pi t}}\)

Consider a rectified sine wave x(t) defined by x(t) = |A sin πt|. Det

1.	Consider a rectified sine wave x(t) defined by x(t) = \|A sin πt\|. Determine its fundamental period and complex exponential Fourier series
A.	\({T_0} = 1\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} - 1}}{e^{jk2\pi t}}\)
B.	\({T_0} = \frac{1}{2}\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} + 1}}{e^{jk2\pi t}}\)
C.	\({T_0} = 1\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} + 1}}{e^{jk2\pi t}}\)
D.	\({T_0} = \frac{1}{2}\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} - 1}}{e^{jk2\pi t}}\)
Answer» B. \({T_0} = \frac{1}{2}\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} + 1}}{e^{jk2\pi t}}\)

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