Wiley signals and systems e book TLFe BO 314

12.2. Some Siinple Seqiiences

299

1

1

2

Figure 12.4: Examples of expctrieril;ial secperices

E x ~ ~ p 12.1
le

T w o exainples for uiiilat,eral exponential sequiices with real values are given by
(12.10) and (12,11), arid illustrated in Figure 12.4.

( 12.10)

(12.11)
For b o t ~ exponential
i
series X = I and 1: = - 1112. TIX arigular frequency II ~ i a s
the values 52 = 0 and I2 = n respectively. Both srries are the same except the
signs before the odd valucts.

In contrast to continuous mqmiicntial fuiictioiis, tiiffcwnt values of tlre nngitlsr
frequency R can lead to the hame exponential series. As eJRk is only etaluated for
integers k , adding multiples of 2n to 0 does not change the sequence:
p

k

--e

j(62L27r)k

(12.12)