Simple question [Signals and Systems]

maverick280857

Hi

The following question is from Oppenheim/Wilsky/Nawab chapter 1.

Consider a periodic signal

[tex]x(t) = 1[/tex] for [tex]0 \leq t \leq 1[/tex]
[tex]x(t) = -2 [/tex] for [tex]1 < t <2[/tex]

with period [itex]T = 2[/itex]. The derivative of this signal is related to the impulse train

[tex]g(t) = \sum_{k = -\infty}^{\infty}\delte(t-2k)[/tex]

with period T = 2. It can be shown that

[tex]\frac{dx(t)}{dt} = A_{1}g(t-t_{1}) + A_{2}g(t-t_{2})[/tex]

Determine the values of [itex]A_{1}[/itex], [itex]t_{1}[/itex], [itex]A_{2}[/itex], and [itex]t_{2}[/itex].

I got stuck with this one. Anyway here's my solution. Would appreciate any help in solving the problem.

[tex]x(t) = \sum_{k = -\infty}^{\infty}(u(t-2k) - u(t-2k-1)) + (-2)(u(t-2k-1) - u(t-2k-2))[/tex]

so

[tex]x(t) = \sum_{k = -\infty}^{\infty}u(t-2k) - 3\sum_{k = -\infty}^{\infty}u(t-2k-1)) -2\sum_{k = -\infty}^{\infty}u(t-2k-2) [/tex]

so

[tex]\frac{dx}{dt} = g(t) - 3g(t-1) - g(t-2)[/tex]

which is wrong...

maverick280857

Okay I got it graphically, but what if I want to do it algebraically?