This preview shows page 1. Sign up to view the full content.
Unformatted text preview: gnal, depicted in
Fig. 8.1, is t herefore a sequence of numbers. This signal may be denoted by f (kT)
a nd viewed a s a function of time t where signal values are specified a t t = kT.
I t m ay also b e d enoted by f [k] a nd viewed as a function of k (k, integer). For
instance, a continuoustime exponential f (t) = e  t , when sampled every T = 0.1
second, r esults in a discretetime signal f (kT) given by D iscretetime signals arise naturally in situations which are inherently discretetime, such as population studies, amortization problems, national income models,
a nd r adar tracking. T hey may also arise as a result of sampling continuoustime
signals in sampled d ata systems, digital filtering, and so on. Digital filtering is a
p articularly interesting application in which continuoustime signals are processed
by discretetime systems, using appropriate interfaces a t t he i nput a nd o utput, as
illustrated in Fig. 8.2. A continuoustime signal f (t) is first sampled to convert it
into a discretetime signal f [k], which is t hen processed by a discretetime system
t o yield t he o utput y[k]. A c ontinuoustime signal y(t) is finally constructed from
y[k]. We shall use t he n otations C /D a nd D /C for continuoustodiscretetime a nd
discretetocontinuoustime conversion. Using the interfaces in this manner, we can
process a continuoustime signal with a n a ppropriate discretetime system. As we
shall see l ater in our discussion, discretetime systems have several advantages over
continuoustime systems. For this reason, t here is a n accelerating t rend toward
processing continuoustime signals with discretetime systems. ~ \ It.. ~ 1 k~ jrrlrrrlIl! t. Discrete to / y ( I) Continuous ole f (kT) = e  kT = e  O. 1k
Clearly, t his signal is a function of k a nd may be expressed as J[k]. We c an plot this
signal as a function of t o r as a function of k (k, integer). T he r epresentation f [k] is
m ore convenient and will be followed throughout this book. A discretetime signal
therefore m ay b e viewed as a sequence of numbers, and a discretetime system may
be seen as processing a sequence of numbers f [k] a nd yielding as o utput a nother
sequence of numbers y[k].
540 F ig. 8 .2 Processing a continuoustime signal by a discretetime system. 8.2 Some Useful DiscreteTime Signal Models We now discuss some i mportant d iscretetime signal models which are encountered frequently in t he s tudy of discretetime signals a nd systems. 8 Discretetime Signals a nd Systems 542 543 8.2 Some Useful Discretetime Signal models (a) (b) k m (a) Fig. 8.3 Discretetime impulse function. 1. D iscrete Time Impulse Function 8[k] T he d iscretetime counterpart of the continuoustime impulse function 8(t) is
8[kJ, defined by 8[k] = g k =O
k lO 3. Discrete Time Exponential yk A continuoustime exponential {~ I f we w ant a signal t o s tart a t k = 0 (so t hat i t has a zero value for all k < 0),
we need o nly multiply the signal with u[k]. 4 6 k Fig. 8 .4 A discretetime unit step functi...
View
Full
Document
This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.
 Spring '13
 Bayliss
 Signal Processing, The Land

Click to edit the document details