By Mrinal Mandal, Amir Asif
This textbook provides an creation to the elemental ideas of continuous-time (CT) and discrete-time (DT) signs and platforms, treating them individually in a pedagogical and self-contained demeanour. Emphasis is at the simple sign processing ideas, with underlying recommendations illustrated utilizing sensible examples from sign processing, multimedia communications, and bioinformatics. Following introductory chapters, the textual content is separated into components. half I covers the theories, concepts, and functions of CT indications and structures and half II discusses those issues for DT, in order that the 2 will be taught independently or jointly. Accompanying the ebook is a CD-ROM containing MATLAB code, audio clips, pictures, interactive courses, and sign animations. With over three hundred illustrations, 285 labored examples and 385 homework difficulties, this textbook is a perfect creation to the topic for undergraduates in electric and machine engineering. extra assets, together with suggestions for teachers, can be found on-line at www.cambridge.org/9780521854559.
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Extra info for Continuous and discrete time signals and systems
Consider a CT signal φ(t) obtained by shifting another signal x(t) by T time units. The time-shifted signal φ(t) is expressed as follows: φ(t) = x(t + T ). P1: RPU/XXX P2: RPU/XXX CUUK852-Mandal & Asif QC: RPU/XXX May 25, 2007 T1: RPU 18:7 36 Part I Introduction to signals and systems 2 x(t − 3) x(t) 2 t t −8 −6 −4 −2 (a) Fig. 21. Time shifting of a CT signal. (a) Original CT signal x(t ). (b) Time-delayed version x(t − 3) of the CT signal x(t ). and (c) Time-advanced version x(t + 3) of the CT signal x(t ).
In other words, the real and imaginary parts of the complex exponential are pure sinusoids. 14 shows the real and imaginary parts of the complex exponential function. 5)t] for −4 ≤ t ≤ 4. 5t × e j4πt . 5t sin(4π t). To plot the real component, we multiply the waveform of a cosine function with ω0 = 4π , as shown in Fig. 5t). The resulting plot is shown in Fig. 15(a). Similarly, the imaginary component is plotted by multiplying the waveform of a sine function with ω0 = 4π, as shown in Fig. 5t). The resulting plot is shown in Fig.
The waveforms of x[k − 4] and x[k + 4] are identical to that of x[k]. The time-delayed signal x[k− 4] is obtained by shifting x[k] towards the right-hand side by four time units. The time-advanced signal x[k + 4] is obtained by shifting x[k] towards the left-hand side by four time units. P1: RPU/XXX P2: RPU/XXX CUUK852-Mandal & Asif QC: RPU/XXX May 25, 2007 T1: RPU 18:7 37 1 Introduction to signals x[k − 4] x[k] 1 −8 −6 −4 −2 (a) 2 3 1 k 0 2 4 6 −8 8 −6 −4 2 3 k −2 2 0 4 6 8 4 6 8 (b) x[k + 4] Fig.