12, The Spectrum of Discrete Signals 298 iscrete Step finction The discrete unit step function from Figure 12.3 is defined by (12.6) The relationship betwcwi the nnit step function arid the unit impidlse corresponds to the tquivalcrit for continuous signals: (12.7) I [ k ]= E[k] - Elk - 1) I (12.8) Iiit,egration in the coiitiriuoiis cabe corresponds bo discrete surnmation and differentiation of coritinuous signals corresponds to subtracting the neighbouring valr Le in the discrete case k Figure 12.3: Discrete unit step function 2.2.3 Exponential Sequences ExponenLial aegiwnces are in general complex sequences of the form (12.9) X is the complex amplitude, C is the damping (w1stitnt, arid K! is t,he angular frequency Discrete cxporieiitial sequences axe often characterised directly by giviiig theii base, especially if they will be initerprcted a s tlx iinpiihe K ~ S ~ W IofWa discrct e system