Wiley signals and systems e book TLFe BO 313

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 6 [ 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.