Question

1. On how to use the analysis or synthesis equations to calculate the Fourier transform of signal $x(t)$ or the inverse Fourier transform of $X(j\omega)$. (a) $x(t) = e^{-2|t-1|}$ (b) $x(t) = \frac{d}{dt}\{u(-2 - t) + u(t - 2)\}$ (c) $x(t) = 1 + cos(6\pi t + \frac{\pi}{8})$ (Note that this is a periodic signal) (d) $X(j\omega)$ is complex where $|X(j\omega)| = 2\{u(\omega + 3) - u(\omega - 3)\}$ $\angle X(j\omega) = -\frac{3}{2}\omega + \pi$

          1. On how to use the analysis or synthesis equations to calculate the Fourier
transform of signal $x(t)$ or the inverse Fourier transform of $X(j\omega)$. 
(a) $x(t) = e^{-2|t-1|}$ 
(b) $x(t) = \frac{d}{dt}\{u(-2 - t) + u(t - 2)\}$ 
(c) $x(t) = 1 + cos(6\pi t + \frac{\pi}{8})$ (Note that this is a periodic signal)
(d) $X(j\omega)$ is complex where
$|X(j\omega)| = 2\{u(\omega + 3) - u(\omega - 3)\}$
$\angle X(j\omega) = -\frac{3}{2}\omega + \pi$

$1. On how to use the analysis or synthesis equations to calculate the Fourier transform of signal x(t) or the inverse Fourier transform of X(jω). (a) x(t) = e^-2|t-1| (b) x(t) = (d)/(dt){u(-2 - t) + u(t - 2)} (c) x(t) = 1 + cos(6π t + (π)/(8)) (Note that this is a periodic signal) (d) X(jω) is complex where |X(jω)| = 2{u(ω + 3) - u(ω - 3)} ∠ X(jω) = -(3)/(2)ω + π$

Added by Kevin J.

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