Question

Let y(t)= r(t) - 2r(t-1) + r(t-3) + u(t-4), where r(t) is the

ramp function.
a) plot y(t)
b) plot z(t) = y(2t-1)
c) plot y'(t)
d) calculate the energy of y(t)
note: r(t) = t for t ≥ 0 and 0 for t &l

Answer 1

To plot y(t), substitute the ramp function r(t) into the given equation for y(t). Then, plot z(t) by substituting 2t-1 into t in the previous equation. To calculate the energy of y(t), integrate the squared absolute value of y(t) over its domain.

Step-by-step explanation:

To plot y(t), we need to substitute the ramp function r(t) into the given equation for y(t). For t < 0, r(t) = 0 because the ramp function is defined as 0 for t < 0. For t ≥ 0, r(t) = t. Therefore, y(t) = t - 2(t-1) + (t-3) + u(t-4).

To plot z(t), we substitute 2t-1 into t in the previous equation. z(t) = (2t-1) - 2[(2t-1)-1] + [(2t-1)-3] + u[(2t-1)-4].

To plot y'(t), we need to find the derivative of y(t) with respect to t. And to calculate the energy of y(t), we must integrate the squared absolute value of y(t) over its domain.