A basic result from Section 4 is that the response of an LTI system is given by convolution of the input and the impulse response of the system. In this section we present an alternative representation for signals and LTI systems. The Laplace transform is introduced to represent continuous-time signals in the s-domain (s is a complex variable), and the concept of the system function for a continuous-time LTI system is described. Many useful insights into the properties of continuous-time LTI systems, as well as the study of many problems involving LTI systems, can be provided by application of the Laplace transform technique.<\/p>\n
We also present the z-transform, which is the discrete-time counterpart of the Laplace transform. The z-transform is introduced to represent discrete-time signals (or sequences) in the z-domain (z is a complex variable), and the concept of the system function for a discrete-time LTI system will be described. The Laplace transform converts integrodifferential equations into algebraic equations. In a similar manner, the z-transform converts difference equations into algebraic equations, thereby simplifying the analysis of discrete-time systems. The properties of the z-transform closely parallel those of the Laplace transform.<\/p>\n
Neljanda osa p\u00f5hitulemusena selgus, et LNI s\u00fcsteemi v\u00e4ljundi saab arvutada selle impulsskoste ja sisendi sidumsummana. Viiendas osas tutvustatakse signaalide ja LNI s\u00fcsteemide \u00fchte v\u00f5imalikku esitusviisi (teisendustehet). Laplace teisendus esitab suvalist signaali v\u00f5i s\u00fcsteemi komplekses s-ruumis. Tutvustatakse s\u00fcsteemi funktsiooni m\u00f5istet pidevate LNI s\u00fcsteemide kirjeldamiseks. Laplace teisenduse teostamise j\u00e4rel on paljusid signaalide ja LNI s\u00fcsteemide omadusi oluliselt lihtsam n\u00e4ha kui aegesitust uurides. Defineeritakse z-teisendus, mis on Laplace teisenduse analoog diskreetse argumendiga signaalide ja LNI s\u00fcsteemide jaoks. Z-teisendus esitab diskreetse argumendiga signaale v\u00f5i LNI s\u00fcsteeme komplekses z-ruumis. Laplace teisenduse abil saab teisendada integraalsed diferentsiaalsed v\u00f5rrandid algebralisteks v\u00f5rranditeks ning neid seel\u00e4bi oluliselt lihtsustada. Z-teisenduse omadused on Laplace teisenduse omadustega analoogsed.<\/p>\n
Video #1 \u2013 Laplace transform <\/p>
<\/strong><\/p>\n