Signály, časové řady a lineární systémy
| Title in English | Signals, time-series, and linear systems |
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| Authors | |
| Year of publication | 2012 |
| MU Faculty or unit | |
| Citation | |
| Description | The book “Signals, Time Series, and Linear Systems” provides introduction into the field of time data processing. It was written with support of the ESF grant No. CZ.1.07/2.2.00/07.0318 “Multidisciplinary Innovation of Study in Computational Biology”. The first chapter aims to be inspiring and motivating, introduces fundamental terms and numerous practical examples, in which the knowledge obtained hereinafter can be employed. Two subsequent chapters deal with methods for description of time functions and series. Time functions and series in time domain are described at first. Terms convolution and corre-lation are explained in very details. The term frequency spectrum is subsequently introduced and methods for transformation from time to frequency domain and vice versa are described. Terms such as Fourier series, Fourier transform, Fourier transform in discrete time, and dis-crete Fourier transform, respectively, are defined for this purpose. Ways of their application for basic functions and series are described and typical shapes of frequency spectra for spe-cific selected functions and series are shown, as well. The second part of this publication is focused on linear system operating in both continuous and discrete time mode. Basic methods of input/output description of linear systems are presented by means of differential and difference equations, respectively, transfer functions and their properties, by means of frequency and time (impulse, transient) responses. The last chapter deals with fundamental computational structures of linear systems. Basic forms of system connections – serial, parallel and feed-back connection – are explained and the chapter is concluded with description of fundamental continuous and discrete realizations, such as proportional, integrative, derivative and real derivative blocks for continuous time. For the discrete time, the chapter particularly emphasizes basic structures with moving average and autoregressive systems. The lessons are often accompanied with illustrative examples that explain principle of the described methods. |
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