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

# Y t c linear system analysis using t he bilateral

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: l by which a signal is expressed as a sum o f everlasting exponentials est. T he relati:ve a mount o f a c omponent est is F (s). Therefore F (s), t he Laplace transform of f (t), r epresents t he s pectrum of exponential components of f (t). Moreover, H (s) is t he s ystem response (or gain) t o a s pectral component est, a nd t he o utput signal s pectrum is t he i nput s pectrum F (s) t imes t he s pectral response (gain) H (s) [yes) = F(s)H(s)J. T he Laplace transform changes integro-differential equations of L TIC systems into algebraic equations. Therefore, solving these integro-differential equations reduces t o solving algebraic equations. T he Laplace transform method cannot generally be used for time-varying p arameter s ystems or for nonlinear systems. T he t ransfer function of a system may also be defined as a ratio of t he Laplace transform of t he o utput t o t he Laplace transform of t he i nput when all initial conditions are zero (system in zero state). I f F (s) is t he Laplace transform of t he i nput f (t) a nd Y (s) is t he Laplace transform of t he corresponding o utput yet) (when all initial conditions are zero), t hen y es) = F (s)H(s), where H (s) is t he system transfer function. T he s ystem transfer function H (s) is t he Laplace transform of the system impulse response h (t). Like t he impulse response h (t), t he t ransfer function H (s) is also a n e xternal description of t he s ystem. Electrical circuit analysis can also be carried o ut by using a transformed circuit method, in which all signals (voltages a nd c urrents) are represented by their Laplace transforms, all elements by their impedances (or admittances), a nd initial conditions by their equivalent sources (initial condition generators). In this method, a network can be analyzed as if it were a resistive circuit. Large systems can b e considered as suitably interconnected subsystems represented by blocks. Each subsystem, being a smaller system, can b e readily analyzed a nd r epresented by its i nput-output relationship, such as its transfer function. Analysis o f large systems can be carried o ut w ith t he knowledge of i nput-output relationships of its subsystems a nd t he n ature o f i nterconnection o f various subsystems. LTIC s ystems can be realized by scalar multipliers, summers, a nd i ntegrators. A given transfer function can be synthesized in many different ways. Canonical, cascade, a nd parallel forms of realization are discussed. I n p ractice, all t he building blocks (scalar multipliers, summers, a nd i ntegrators) can be obtained from operational amplifiers. Feedback systems are closed-loop systems mainly used t o c ounteract t he effects of unpredictable variations in t he s ystem parameters, t he load, a nd t he environment. Such systems are designed for a specified speed a nd t he s teady-state error. For speed, t he useful transient parameters are rise time, peak time, a nd s ettling time. Percent overshoot indicates how smoothly t he system o utput rises to its final value. We can relate t he s tea...
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