Signal Processing and Linear Systems-B.P.Lathi copy

# In this case t he o utput a t any i nstant t does not

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Unformatted text preview: rson) who can give t he a nswers immediately, or go t o a wise m an a nd allow him a delay of one year t o give us the answer! I f t he wise m an is t ruly wise, he may even be able t o shrewdly guess t he future very closely with a delay of less t han a year by studying trends. Such is t he case with noncausal s ystems-nothing more a nd n othing less. e::. E xercise E Ll5 87 Lumped-Parameter and Distributed-Parameter Systems I n t he s tudy of electrical systems, we make use of voltage-current relationships for various components ( Ohm's law, for example). I n doing so, we implicitly a ssume' t hat t he c urrent in any system component (resistor, inductor, etc.) is t he s ame a t every point throughout t hat c omponent. Thus, we assume t hat electrical signals are propagated instantaneously throughout t he system. In reality, however, electrical signals are electromagnetic space waves requiring some finite propagation time. An electric current, for example, propagates through a component with a finite velocity a nd therefore may exhibit different values a t different locations in t he same component. Thus, a n electric current is a function not only of time b ut also of space. However, if t he physical dimensions of a component are small compared t o t he wavelength of t he signal propagated, we may assume t hat t he c urrent is c onstant throughout t he component. T his is t he a ssumption made in l umped-parameter s ystems, where each component is r egarded as being lumped a t one point in space. Such a n a ssumption is justified a t lower frequencies (higher wavelength). Therefore, in lumped-parameter models, signals can be assumed t o b e functions of time alone. For such systems, t he s ystem equations require only one independent variable (time) a nd therefore are ordinary differential equations. In contrast, for d istributed-parameter s ystems such as transmission lines, waveguides, antennas, a nd microwave tubes, t he s ystem dimensions cannot be assumed t o b e small compared to t he wavelengths of t he signals; thus the lumpedparameter a ssumption breaks down. T he signals here are functions of space as well as of time, leading t o m athematical models consisting of partial differential equations. 3 T he discussion in this book will be restricted to lumped-parameter systems only. 1 .7-6 Continuous-Time and Discrete-Time Systems D istinction between discrete-time a nd continuous-time signals is discussed in Sec. 1.2-1. Systems whose inputs a nd o utputs a re continuous-time signals are c ontinuous-time s ystems. O n t he o ther hand, systems whose inputs and outputs a re discrete-time signals are d iscrete-time s ystems. I f a c ontinuous-time signal is sampled, t he r esulting signal is a discrete-time signal. We can process a continuous-time signal by processing its samples with a discrete-time system. 1 .7-7 Analog and Digital Systems Analog a nd digital signals are discussed in Sec. 1.2-2. A system whose i nput a nd o utput signals are analog is a n a nalog s ystem; a s ystem whose i nput a nd o utput signals are digital is a d igital s ystem. A digital computer is a n example of a digital (binary) system. Observe t hat a digital computer is a n e xample of a system t hat is digital as well...
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## This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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