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

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
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.

Ask a homework question - tutors are online