Question 5.9: Characterize the composite waveform generated by v(t) = VAu(......

The first term in this waveform is simply a step function of amplitude V_A that occurs at t = 0. The second term involves the function u(−t), whose waveform requires some discussion. Strictly speaking, the general step function u(x) is unity when x > 0 and zero when x < 0. That is, u(x) is unity when its argument is positive and zero when it is negative. Under this rule the function u(−t) is unity when −t > 0 and zero when −t < 0, that is,

u(−t) = \begin{cases} 1 \quad for  t <0  \\ 0 \quad for  t > 0 \end{cases}

which is the reverse of the step function u(t). Figure 5–27 shows how the two components combine to produce a composite waveform that extends indefinitely in both directions and has a jump discontinuity of 2V_A at t = 0. This composite waveform is called a signum function.