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Unformatted text preview: reating zero-valued
samples in between. We c an reconstruct t he zero-valued samples using interpolation
from t he nonzero samples. T he i nterpolation, thus, creates additional samples in
between using t he i nterpolation process. For this reason, this operation is called
i nterpolation o r upsampling.
D iscrete-time systems may be used t o process discrete-time signals, or t o process continuous-time signals using appropriate interfaces a t t he i nput a nd o utput.
At t he i nput, t he continuous-time i nput signal is c onverted into a discrete-time signal t hrough sampling. T he r esulting discrete-time signal is now processed by t he
discrete-time system yielding a discrete-time o utput. T he o utput interface now converts t he d iscrete-time o utput i nto a continuous-time o utput. Discrete-time systems
are characterized by difference equations.
Discrete-time systems can be realized by using scalar multipliers, summers,
and time delays. These operations can be readily performed by digital computers. T ime delays also can be obtained from charge coupled devices ( CCD), b ucket
brigade devices (BBD), a nd surface acoustic wave devices (SAW). Several a dvantages of discrete-time systems over continuous-time systems are discussed in Sec.
8.5. Because of these advantages, discrete-time systems are replacing continuoustime systems in several applications. References
1. Milstein, L. B., and P.K. Das, "Surface Acoustic wave Devices," I EEE Communication Society Magazine, vol. 17, N o.5, p p. 25-33, September 1979. Problems
5k 8.2-1 The following signals are in the form e Ak . Express them in the form - /: ( a) e -O.
( b) eO. 5k (c) e -i"k ( d) e i"k. In each case show the locations of A and'"Y in the
complex plane. Verify t hat an exponential is growing if '"Y lies outside the unit circle
(or if A lies in the RHP), is decaying if'"Y lies within the unit circle (or if A lies in the 5 70 8 D iscrete-time Signals a nd S ystems
L HP), a nd h as a c onstant a mplitude i f " i lies o n t he u nit circle (or i f A lies o n t he
i maginary axis). 8 .2-2 R epeat P rob. 8.2-1 for t he e xponentials ( a)
( d) e (I-J,,)k ( e) e -(1+jt)k ( f) e (I-ji)k . ( b) e -(1+j,,)k ( e) D etermine t he f undamental r ange frequency f lf for t he s inusoids o f t he f requencies
f l = (a) O.B71" ( b) 1.271" (c) 6.9 (d) 3.771" (e) 22.971". F or e ach case, d etermine also t he
lowest frequency which c an b e used t o d escribe t hese s inusoids. + f) + v'3 cos (1.471"k + i ) = 8 .2-7 E xpress t he following exponentials in t he form ( a) ej (8.2"k+8) ( b) e 3 4"k 2 cos (0.671"k - j e (ilk+8), 8 .3-1 A d iscrete-time p rocessor uses a s ampling i nterval T = 0 .5I's. W hat is t he h ighest
frequency o f a s ignal t hat c an b e p rocessed w ith t his p rocessor w ithout a liasing? I f a
s ignal o f f requency 2 MHz is s ampled b y this processor, w hat w ould b e t he ( aliased)
frequency o f t he...
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