Observing that $x_c(t) = Re(\bar{x}(t)) = \frac{\bar{x}(t) + \bar{x}^*(t)}{2}$, show that $X_c(f) = \frac{X(f) + X^*(-f)}{2}$. Observing that $x_s(t) = Im(\bar{x}(t)) = \frac{\bar{x}(t) - \bar{x}^*(t)}{2j}$, derive a relation between $X_s(f)$ and $\bar{X}(f)$.
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It seems that (t) represents a function, and Im((t) represents the imaginary part of that function. So, we can rewrite the given equation as: Im((t) = 2j Now, let's break down the equation further. The imaginary part of a complex number is the coefficient of the Show more…
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