Unit step signal and ramp signal

Unit step signal

A signal, which satisfies the following two conditions −

• U(t)=1(whent≥0)and$U(t)=1(whent\ge 0)and$
• U(t)=0(whent<0)$U(t)=0(whent<0)$

is known as a unit step signal.

It has the property of showing discontinuity at t = 0. At the point of discontinuity, the signal value is given by the average of signal value. This signal has been taken just before and after the point of discontinuity (according to Gibb’s Phenomena).

If we add a step signal to another step signal that is time scaled, then the result will be unity. It is a power type signal and the value of power is 0.5. The RMS (Root mean square) value is 0.707 and its average value is also 0.5

Ramp Signal

Integration of step signal results in a Ramp signal. It is represented by r(t). Ramp signal also satisfies the condition r(t)=∫t−∞U(t)dt=tU(t)$r(t)={\int }_{-\mathrm{\infty }}^{t}U(t)dt=tU(t)$. It is neither energy nor power (NENP) type signal.