This preview shows page 1. Sign up to view the full content.
Unformatted text preview: reating zerovalued
samples in between. We c an reconstruct t he zerovalued 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 iscretetime systems may be used t o process discretetime signals, or t o process continuoustime signals using appropriate interfaces a t t he i nput a nd o utput.
At t he i nput, t he continuoustime i nput signal is c onverted into a discretetime signal t hrough sampling. T he r esulting discretetime signal is now processed by t he
discretetime system yielding a discretetime o utput. T he o utput interface now converts t he d iscretetime o utput i nto a continuoustime o utput. Discretetime systems
are characterized by difference equations.
Discretetime 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 discretetime systems over continuoustime systems are discussed in Sec.
8.5. Because of these advantages, discretetime 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. 2533, September 1979. Problems
5k 8.21 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 iscretetime 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 .22 R epeat P rob. 8.21 for t he e xponentials ( a)
( d) e (IJ,,)k ( e) e (1+jt)k ( f) e (Iji)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 .27 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 .31 A d iscretetime 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...
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