barcode generator for ssrs An LSI system with unit sample response h(n) = anu(n)will be stable whenever la1 < 1, because in Software

Encoding Code128 in Software An LSI system with unit sample response h(n) = anu(n)will be stable whenever la1 < 1, because

EXAMPLE 1.3.5
Decode USS Code 128 In None
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
Encode Code 128 In None
Using Barcode creator for Software Control to generate, create Code 128B image in Software applications.
An LSI system with unit sample response h(n) = anu(n)will be stable whenever la1 < 1, because
Code 128A Reader In None
Using Barcode scanner for Software Control to read, scan read, scan image in Software applications.
Drawing ANSI/AIM Code 128 In Visual C#
Using Barcode drawer for VS .NET Control to generate, create Code 128C image in Visual Studio .NET applications.
The system described by the equation y ( n ) = nx(n), on the other hand, is not stable because the response to a unit step,
Encoding Code 128 Code Set A In .NET
Using Barcode creator for ASP.NET Control to generate, create Code 128 Code Set A image in ASP.NET applications.
Code 128 Code Set A Generation In VS .NET
Using Barcode maker for .NET Control to generate, create USS Code 128 image in Visual Studio .NET applications.
x(n) = u(n), is y(n) = nu(n), which is unbounded.
Encode Code 128A In VB.NET
Using Barcode creation for .NET framework Control to generate, create Code-128 image in Visual Studio .NET applications.
DataMatrix Creation In None
Using Barcode creation for Software Control to generate, create DataMatrix image in Software applications.
CHAP. 11
Printing EAN128 In None
Using Barcode creator for Software Control to generate, create GTIN - 128 image in Software applications.
Generate EAN-13 Supplement 5 In None
Using Barcode encoder for Software Control to generate, create UPC - 13 image in Software applications.
lnvertibility
Painting GS1 - 12 In None
Using Barcode encoder for Software Control to generate, create UPC A image in Software applications.
Encode Barcode In None
Using Barcode printer for Software Control to generate, create bar code image in Software applications.
SIGNALS AND SYSTEMS
EAN-8 Supplement 2 Add-On Generator In None
Using Barcode printer for Software Control to generate, create European Article Number 8 image in Software applications.
Making Code 128 Code Set C In Java
Using Barcode creation for Android Control to generate, create Code 128 image in Android applications.
A system property that is important in applications such as channel equalization and deconvolutionis invertibility. A system is said to be invertible if the input to the system may be uniquely determined from the output. In order for a system to be invertible, it is necessary for distinct inputs to produce distinct outputs. In other words, given any two inputs x l ( n )and xz(n) with x l ( n ) # xz(n),it must be true that yl(n) # y2(n).
Barcode Creation In Objective-C
Using Barcode drawer for iPhone Control to generate, create bar code image in iPhone applications.
Generating Linear In .NET
Using Barcode drawer for .NET framework Control to generate, create Linear Barcode image in .NET applications.
EXAMPLE 1.3.6
ECC200 Scanner In Java
Using Barcode scanner for Java Control to read, scan read, scan image in Java applications.
Code 128B Drawer In Objective-C
Using Barcode generation for iPad Control to generate, create Code 128 Code Set B image in iPad applications.
The system defined by y(n) = x(n)g(n) is invertible if and only if g(n) from y(n) as follows:
ANSI/AIM Code 128 Drawer In Java
Using Barcode drawer for BIRT Control to generate, create Code128 image in Eclipse BIRT applications.
Encode UCC - 12 In Visual C#
Using Barcode creation for .NET framework Control to generate, create UPC-A image in Visual Studio .NET applications.
# 0 for all n. In particular, given y(n) with g(n) nonzero for all n, x(n) may be recovered
CONVOLUTION
The relationship between the input to a linear shift-invariant system, x(n), and the output, y(n), is given by the convolution sum x(n) * h(n) =
x(k)h(n - k )
Because convolution is fundamental to the analysis and description of LSI systems, in this section we look at the mechanics of performing convolutions. We begin by listing some properties of convolution that may be used to simplify the evaluation of the convolution sum.
1.4.1 Convolution Properties
Convolution is a linear operator and, therefore, has a number of important properties including the commutative, associative, and distributive properties. The definitions and interpretations of these properties are summarized below.
Commutative Property
The commutative property states that the order in which two sequences are convolved is not important. Mathematically, the commutative property is
From a systems point of view, this property states that a system with a unit sample response h(n)and input x ( n ) behaves in exactly the same way as a system with unit sample response x ( n )and an input h(n). This is illustrated in Fig. 1-5(a).
Associative Property
The convolution operator satisfies the associative property, which is
From a systems point of view, the associative property states that if two systems with unit sample responses hl(n) and h2(n)are connected in cascade as shown in Fig. I -5(b), an equivalent system is one that has a unit sample response equal to the convolution of hl ( n )and h2(n):
SIGNALS AND SYSTEMS
[CHAP. 1
(b) The associative property.
( c ) The distributive property.
Fig. 1-5. The interpretation of convolution properties from a systems point of view. Distributive Property
The distributive property of the convolution operator states that
From a systems point of view, this property asserts that if two systems with unit sample responses h l ( n ) and h 2 ( n ) are connected in parallel, as illustrated in Fig. 1-5(c), an equivalent system is one that has a unit sample response equal to the sum of h 1 ( n ) and h2(n):
1A.2
Performing Convolutions
Having considered some of the properties of the convolution operator, we now look at the mechanics of performing convolutions. There are several different approaches that may be used, and the one that is the easiest will depend upon the form and type of sequences that are to be convolved.
Direct Evaluation
When the sequences that are being convolved may be described by simple closed-form mathematical expressions, In the convolution is often most easily performed by directly evaluating the sum given in Eq. ( I 7). performing convolutions directly, it is usually necessary to evaluate finite or infinite sums involving terms of the form anor n a n . Listed in Table 1-1 are closed-form expressions for some of the more commonly encountered series.
EXAMPLE 1.4.1
Let us perform the convolution of the two signals
CHAP. 11
SIGNALS AND SYSTEMS
Table 1-1 Closed-form Expressions for Some Commonly Encountered Series
enan, ,
lal < I
With the direct evaluation of the convolution sum we find
Because u(k) is equal to zero for k < 0 and u(n - k ) is equal to zero for k > n , when n < 0 , there are no nonzero terms in the sum and y ( n ) = 0. On the other hand, if n 3 0,
Therefore,
Copyright © OnBarcode.com . All rights reserved.