Question

Suppose an LTI system is described by the following Linear Constant Coefficient Differential Equation: $\frac{d^2y(t)}{dt^2} + \frac{2dy(t)}{dt} + 3y(t) = \frac{4dx(t)}{dt} - x(t)$ a. Show that the left-hand side of the equation has a Fourier transform that can be expressed as A(W)Y(w), where Y(W) = \{y(t)\} Find A(W). b. Similarly, show that the right-hand side of the equation has a Fourier transform that can be expressed as B(W)X(w), where X(w) = \{x(t)\} c. Show that Y(W) can be expressed as Y(w) = H(W)X(W) and find H(W).

          Suppose an LTI system is described by the following Linear Constant Coefficient Differential
Equation:
$\frac{d^2y(t)}{dt^2} + \frac{2dy(t)}{dt} + 3y(t) = \frac{4dx(t)}{dt} - x(t)$
a. Show that the left-hand side of the equation has a Fourier transform that can be expressed as
A(W)Y(w), where Y(W) = \{y(t)\} Find A(W).
b. Similarly, show that the right-hand side of the equation has a Fourier transform that can be
expressed as B(W)X(w), where X(w) = \{x(t)\}
c. Show that Y(W) can be expressed as Y(w) = H(W)X(W) and find H(W).

$Suppose an LTI system is described by the following Linear Constant Coefficient Differential Equation: (d^2y(t))/(dt^2) + (2dy(t))/(dt) + 3y(t) = (4dx(t))/(dt) - x(t) a. Show that the left-hand side of the equation has a Fourier transform that can be expressed as A(W)Y(w), where Y(W) = {y(t)} Find A(W). b. Similarly, show that the right-hand side of the equation has a Fourier transform that can be expressed as B(W)X(w), where X(w) = {x(t)} c. Show that Y(W) can be expressed as Y(w) = H(W)X(W) and find H(W).$

Added by Alfonso B.

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