A periodic signal can be generated by repeating a period.

(a) Find the function g(t), defined in 0  ‰¤ t ‰¤ 2 only, in terms of basic signals and such that when repeated using a period of 2 generates the periodic signal x(t) shown in Figure 1.22.

(b) Obtain an expression for x(t) in terms of g(t) and shifted versions of it.

(c) Suppose we shift and multiply by a constant the periodic signal x(t) to get new signals y(t) = 2x(t ˆ’ 2), z(t) = x(t + 2), and v(t) = 3x(t) are these signals periodic?

(d) Let then w(t) = dx(t)/dt, and plot it. Is w(t) periodic? If so, determine its fundamental period.

Figure 1.22:

Transcribed Image Text:

r(t) 1. 2.