Because the impulse signal excites all frequencies and the duration of thissignal is infinitely small, you can see the natural response of the system.Figure 3-2 shows that the impulse response of a linear time-invariantsystem is equal to the output y(k) of the system when you apply an impulsesignal to the input u(k) of the system. The impulse response provides thecomplete characteristic information of a system.