Wiley signals and systems e book TLFe BO 341

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I

xaniple 13.5
’i’he z-transform of t h e discrete unit, step kunci,ioil

&[Xi (13.6) is

Z { E [ k ] } = -L.E.- 1 ’ / z />: I

w% iiow arrive directly at, the Lapla,ce transfornl of the coirtinuous-timr signal

by setting 2

= P’.

The h i m e ho~clsfor practical app1icaLioii of ttrr ,z-1 rarisform as for the Laplace
i r ansform, w1iic.h wc liavc. alr
y covered. Calculating 1 he z-i r:~iic;forniof a
qucnce I y maluating tJie w r r
t h r r formula (13.1) only leads to (13.3) for
queiices z[k;(compare Example 13.1).For ott-icr cases, wc try to refei t o
these siniple sciirs by iising sonic gcnclral rules. Thvse grneral rule5 will be summarised by a series of theorerns that h a w n lot of similarities aith the thwrems