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ssrs 2d barcode Signals and Systems in Software
1 Code 128C Scanner In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code128 Maker In None Using Barcode drawer for Software Control to generate, create Code 128C image in Software applications. Signals and Systems
Read Code 128B In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Print ANSI/AIM Code 128 In Visual C#.NET Using Barcode encoder for VS .NET Control to generate, create Code 128B image in .NET applications. 1.1 INTRODUCTION
Code 128C Generation In .NET Using Barcode creation for ASP.NET Control to generate, create Code 128 Code Set B image in ASP.NET applications. Code128 Generator In VS .NET Using Barcode creation for .NET Control to generate, create ANSI/AIM Code 128 image in .NET framework applications. In this chapter we begin our study of digital signal processing by developing the notion of a discretetime signal and a discretetime system. We will concentrate on solving problems related to signal representations, signal manipulations, properties of signals, system classification, and system properties. First, in Sec. 1.2 we define precisely what is meant by a discretetime signal and then develop some basic, yet important, operations that may be performed on these signals. Then, in Sec. 1.3 we consider discretetime systems. Of special importance will be the notions of linearity, shiftinvariance, causality, stability, and invertibility. It will be shown that for systems that are linear and shiftinvariant, the input and output are related by a convolution sum. Properties of the convolution sum and methods for performing convolutions are then discussed in Sec. 1.4. Finally, in Sec. 1.5 we look at discretetime systems that are described in terms of a difference equation. Encode Code 128 Code Set B In VB.NET Using Barcode printer for .NET Control to generate, create Code 128C image in Visual Studio .NET applications. Drawing EAN / UCC  13 In None Using Barcode creation for Software Control to generate, create GS1128 image in Software applications. 1.2 DISCRETETIME SIGNALS
Creating Barcode In None Using Barcode maker for Software Control to generate, create bar code image in Software applications. Barcode Creator In None Using Barcode printer for Software Control to generate, create bar code image in Software applications. A discretetime signal is an indexed sequence of real or complex numbers. Thus, a discretetime signal is a function of an integervalued variable, n, that is denoted by x(n). Although the independent variable n need not necessarily represent "time" (n may, for example, correspond to a spatial coordinate or distance), x(n) is generally referred to as a function of time. A discretetime signal is undefined for noninteger values of n. Therefore, a realvalued signal x(n) will be represented graphically in the form of a lollipop plot as shown in Fig. 1 I. In UPCA Supplement 2 Creation In None Using Barcode drawer for Software Control to generate, create UPCA Supplement 2 image in Software applications. Printing EAN 13 In None Using Barcode generator for Software Control to generate, create EAN13 image in Software applications. Fig. 11. The graphical representation of a discretetime signal x ( n ) . Generate Planet In None Using Barcode drawer for Software Control to generate, create Planet image in Software applications. Paint EAN13 In .NET Using Barcode drawer for .NET Control to generate, create EAN13 image in Visual Studio .NET applications. some problems and applications it is convenient to view x(n) as a vector. Thus, the sequence values x(0) to x(N  1) may often be considered to be the elements of a column vector as follows: Scan Barcode In VS .NET Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. Bar Code Generation In Java Using Barcode maker for Java Control to generate, create barcode image in Java applications. Discretetimesignals are often derived by sampling a continuoustimesignal, such as speech, with an analogtodigital (AID) converter.' For example, a continuoustime signal x,(t) that is sampled at a rate of fs = l/Ts samples per second produces the sampled signal x(n), which is related to xa(t) as follows: Make Code 39 Extended In ObjectiveC Using Barcode generation for iPad Control to generate, create Code39 image in iPad applications. Matrix 2D Barcode Creation In .NET Using Barcode generator for ASP.NET Control to generate, create 2D Barcode image in ASP.NET applications. Not all discretetimesignals, however, are obtained in this manner. Some signals may be consideredto be naturally occurring discretetime sequences because there is no physical analogtodigital converter that is converting an Encode GS1 DataBar Expanded In Visual Studio .NET Using Barcode creator for .NET framework Control to generate, create GS1 DataBar14 image in .NET framework applications. Draw Barcode In ObjectiveC Using Barcode generation for iPhone Control to generate, create bar code image in iPhone applications. Analogtodigital conversion will be discussed in Chap. 3.
SIGNALS AND SYSTEMS
[CHAP. 1
analog signal into a discretetime signal. Examples of signals that fall into this category include daily stock market prices, population statistics, warehouse inventories, and the Wolfer sunspot number^.^ Complex Sequences
In general, a discretetime signal may be complexvalued. In fact, in a number of important applications such as digital communications, complex signals arise naturally. A complex signal may be expressed either in terms of its real and imaginary parts, or in polar form in terms of its magnitude and phase, The magnitude may be derived from the real and imaginary parts as follows: whereas the phase may be found using arg{z(n)) = tan' ImMn)) Re(z(n)) If z(n) is a complex sequence, the complex conjugate, denoted by z*(n), is formed by changing the sign on the imaginary part of z(n): 1.2.2 Some Fundamental Sequences
Although most informationbearing signals of practical interest are complicated functions of time, there are three simple, yet important, discretetime signals that are frequently used in the representation and description of more complicated signals. These are the unit sample, the unit step, and the exponential. The unit sample, denoted by S(n), is defined by S(n) = n=O otherwise
and plays the same role in discretetime signal processing that the unit impulse plays in continuoustime signal processing. The unit step, denoted by u(n), is defined by u(n) = and is related to the unit sample by n 1 0 otherwise
Similarly, a unit sample may be written as a difference of two steps: 2 ~ h Wolfer sunspot number R was introduced by Rudolf Wolf in 1848 as a measure of sunspot activity. Daily records are available back e to 1818 and estimates of monthly means have been made since 1749. There has been much interest in studying the correlation between sunspot activity and terrestrial phenomena such as meteorological data and climatic variations.

