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barcode generator for ssrs CHAP. 11 in Software
CHAP. 11 Read Code128 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Paint Code 128 In None Using Barcode printer for Software Control to generate, create USS Code 128 image in Software applications. SIGNALS AND SYSTEMS
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Encode Code128 In .NET Framework Using Barcode maker for ASP.NET Control to generate, create Code 128 image in ASP.NET applications. Code128 Creator In Visual Studio .NET Using Barcode encoder for .NET framework Control to generate, create Code 128 Code Set C image in .NET framework applications. A discretetime system is a mathematical operator or mapping that transforms one signal (the input) into another signal (the output) by means of a fixed set of rules or operations. The notation T [  ]is used to represent a general system as shown in Fig. 14, in which an input signal x(n) is transformed into an output signal y(n) through the transformation T [ . ] . The inputoutput properties of a system may be specified in any one of a number of different ways. The relationship between the input and output, for example, may be expressed in terms of a concise mathematical rule or function such as Code 128 Generation In VB.NET Using Barcode creator for VS .NET Control to generate, create Code 128 Code Set C image in VS .NET applications. Print Code 128 Code Set A In None Using Barcode generation for Software Control to generate, create Code128 image in Software applications. It is also possible, however, to describe a system in terms of an algorithm that provides a sequence of instructions or operations that is to be applied to the input signal, such as yl(n) = 0.5yl(n  1) 0.25x(n) Barcode Drawer In None Using Barcode creation for Software Control to generate, create bar code image in Software applications. Making Code39 In None Using Barcode encoder for Software Control to generate, create ANSI/AIM Code 39 image in Software applications. + y2(n) = 0.25y2(n  1) + 0.5x(n) ys(n) = 0.4y3(n  1) + 0.5x(n) + y(n) = Y I ( ~ ) y2(n) + ydn) GTIN  128 Creator In None Using Barcode encoder for Software Control to generate, create UCC.EAN  128 image in Software applications. Create Bar Code In None Using Barcode creation for Software Control to generate, create barcode image in Software applications. In some cases, a system may conveniently be specified in terms of a table that defines the set of all possible inputoutput signal pairs of interest. British Royal Mail 4State Customer Barcode Maker In None Using Barcode maker for Software Control to generate, create British Royal Mail 4State Customer Code image in Software applications. Code 39 Extended Encoder In Java Using Barcode printer for Java Control to generate, create Code 39 Extended image in Java applications. Fig. 14. The representation of a discretetimesystem as a transformation T [ . ] that maps an input signal x ( n ) into an output signal y(n). UPCA Creator In Java Using Barcode creation for Java Control to generate, create UPCA image in Java applications. Read Data Matrix In VB.NET Using Barcode reader for VS .NET Control to read, scan read, scan image in .NET framework applications. Discretetime systems may be classified in terms of the properties that they possess. The most common properties of interest include linearity, shiftinvariance, causality, stability, and invertibility. These properties, along with a few others, are described in the following section. EAN 13 Creator In Java Using Barcode printer for BIRT reports Control to generate, create EAN13 Supplement 5 image in BIRT applications. ECC200 Recognizer In Java Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications. 1 .XI
UPC A Encoder In Java Using Barcode creation for Android Control to generate, create GTIN  12 image in Android applications. Creating Code 128B In VB.NET Using Barcode encoder for .NET Control to generate, create Code128 image in Visual Studio .NET applications. System Properties
Memoryless System
The first property is concerned with whether or not a system has memory.
Definition: A system is said to be memoryless if the output at any time n = no depends only on the input at time n = no. In other words, a system is memoryless if, for any no, we are able to determine the value of y(no) given only the value of x(no). EXAMPLE 1.3.1 The system
y(n) = x 2 b ) is memoryless because y(no)depends only on the value of x ( n ) at time no. The system
y(n) = x(n) + x(n  I) on the other hand, is not memoryless because the output at time no depends on the value of the input both at time no and at time no  1. Additivity
SIGNALS AND SYSTEMS
[CHAP. 1
An additive system is one for which the response to a sum of inputs is equal to the sum of the inputs individually. Thus, Definition: A system is said to be additive if
T [ x l ( n )+ x2(n)I = T [ x ~ ( n ) l T[x2(n)l
for any signals X I (n) and x2(n). Homogeneity
A system is said to be homogeneous if scaling the input by a constant results in a scaling of the output by the same amount. Specifically, Definition: A system is said to be homogeneous if
T [cx(n)]= cT [x(n)] for any complex constant c and for any input sequence x(n). EXAMPLE 1.3.2 The system defined by
~ ( n= ) x(n  1 ) x2(n) This system is, however, homogeneous because, for an input c x ( n ) the output is
On the other hand, the system defined by the equation
y(n) =x(n) +x'(n  1 )  I ) ] + [xp(n) + x ; ( n  l ) ] is additive because
[ x ~ ( n ) + x ~ ( n +I[ X I @ )  1) + x A n  I l l * = [xl(n) + x f ( n
However, this system is not homogeneous because the response to c x ( n ) is
T [ c x ( n ) ]= c x ( n ) + c*x*(n  1) + cx*(n  1) which is not the same as
cT[x(n)] = cx(n) Linear Systems
A system that is both additive and homogeneous is said to be linear. Thus, Definition: A system is said to be linear if
T [ a m ( n ) am(n)l =alT[x~(n)l+ azT[xAn)l
for any two inputs xl(n) and x2(n) and for any complex constants a1 and a2.
CHAP. 11
SIGNALS AND SYSTEMS
Linearity greatly simplifies the evaluation of the response of a system to a given input. For example, using the decomposition for x ( n ) given in Eq. (1.4),and using the additivity property, it follows that the output y ( n ) may be written as y(n)=T[x(n)]=T
k=m
x(k)S(nk) Because the coefficients x ( k ) are constants, we may use the homogeneity property to write
k=m
T[x(k)S(nk)] ~ ( n= ) k=ca
T[x(k)G(n k)l =
k=m
x(k)T[S(n k)] If we define h k ( n ) to be the response of the system to a unit sample at time n = k , h k ( n ) = T [S(n  k ) ]

