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barcode generator for ssrs CHAP. 51 in Software
CHAP. 51 Code 128C Decoder In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. ANSI/AIM Code 128 Drawer In None Using Barcode generation for Software Control to generate, create Code 128B image in Software applications. TRANSFORM ANALYSIS OF SYSTEMS
ANSI/AIM Code 128 Decoder In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Code 128A Generator In C# Using Barcode drawer for Visual Studio .NET Control to generate, create ANSI/AIM Code 128 image in VS .NET applications. Fig. 52. Evaluating the frequency response geometrically from the
Code 128A Drawer In .NET Using Barcode printer for ASP.NET Control to generate, create Code 128 Code Set A image in ASP.NET applications. Code 128A Creator In .NET Framework Using Barcode drawer for .NET framework Control to generate, create Code128 image in .NET applications. poles and zeros of the system function.
Drawing USS Code 128 In VB.NET Using Barcode creator for .NET framework Control to generate, create Code 128 Code Set B image in VS .NET applications. Creating Code39 In None Using Barcode printer for Software Control to generate, create USS Code 39 image in Software applications. where 0, is the angle subtended by the vector from the zero at z = ,Ek to the unit circle at z = eJw(see Fig. 52). Similarly, for each term in the denominator Printing Data Matrix In None Using Barcode encoder for Software Control to generate, create DataMatrix image in Software applications. Creating GS1 128 In None Using Barcode maker for Software Control to generate, create UCC  12 image in Software applications. where Q2 is the angle of the vector from the pole at z = a!k to the unit circle at z = eJW.When a pole (zero) is close to the unit circle, the phase decreases (increases) rapidly as we move past the pole (zero). Because the group delay is the negative of the derivative of the phase, this implies that the group delay is large and positive close to a pole and large and negative when close to a zero. Bar Code Encoder In None Using Barcode maker for Software Control to generate, create barcode image in Software applications. Drawing Code 128A In None Using Barcode encoder for Software Control to generate, create Code 128A image in Software applications. 5.3 SYSTEMS WITH LINEAR PHASE
Creating ISSN In None Using Barcode generator for Software Control to generate, create ISSN  13 image in Software applications. Making USS Code 128 In Visual C#.NET Using Barcode generator for .NET framework Control to generate, create Code128 image in Visual Studio .NET applications. A linear shiftinvariant system is said to have linear phase if the frequency response has the form
Bar Code Maker In .NET Using Barcode printer for ASP.NET Control to generate, create bar code image in ASP.NET applications. USS Code 39 Drawer In ObjectiveC Using Barcode creator for iPhone Control to generate, create Code 39 image in iPhone applications. H (ejw)= I H (eiW)1ejaw
Make UPCA Supplement 5 In VB.NET Using Barcode generator for VS .NET Control to generate, create UPCA image in .NET applications. Bar Code Reader In VS .NET Using Barcode scanner for .NET framework Control to read, scan read, scan image in .NET framework applications. where a! is a real number. Thus, linear phase systems have a constant group delay, GTIN  12 Generation In ObjectiveC Using Barcode creation for iPhone Control to generate, create UCC  12 image in iPhone applications. Code 39 Creator In None Using Barcode drawer for Online Control to generate, create Code 3/9 image in Online applications. In some applications, one is interested in designing systems that have what is referred to as generalized linear phase. A system is said to have generalized linear phase if the frequency response has the form where A(ejw)is a realvalued (possibly bipolar) function of w , and p is a constant. Often, the term linearphase is used to denote a system that has either linear or generalized linear phase. EXAMPLE 5.3.1
Consider the FIR system with a unit sample response
h(n) = n=0,1, ..., N
else
The frequency response is
TRANSFORM ANALYSIS OF SYSTEMS
[CHAP. 5
Therefore, this system has generalized linear phase, with a = N / 2 and
= 0. In order for a causal system with a rational system function to have linear phase, the unit sample response must be finite in length. Therefore, IIR filters cannot have (generalized) linear phase. For an FIR filter with a realvalued unit sample response of length N I , a sufficient condition for this filter to have generalized linear phase is that the unit sample response be symmetric, In this case, cr = N / 2 and B = 0 or YC. Another sufficient condition is that h(n) be antisymmetric, which corresponds to the case in which cr = N / 2 and B = n / 2 or 3x12. Linear phase filters may be classified into four types, depending upon whether h(n) is symmetric or antisymmetric and whether N is even or odd. Each of these filters has specific constraints on the locations of the zeros in H ( z ) which, in turn, place constraints on the frequency response magnitude. For each of these types, which are described below, it is assumed that h(n) is realvalued, and that h(0) is the first nonzero value of h(n). Q p e I Linear Phase Filters
A type I linear phase filter has a symmetric unit sample response, and N is even. The center of symmetry is about the point cr = N/2, which is an integer, as illustrated in Fig. 53(a). h(n) It Center of symmetry
h(n) Center of symmetry
.I. I I I
 1 L s ;a
( 6 )Type 11 filter.
I I \ I
h(n) I+ I I I I
c Center of symmetry
Center of symmetry
 1 I t 3
(c)Type 111 filter.
(d)v p e IV filter.
Fig. 53. Symmetries in the unit sample response for generalized linear phase systems.
CHAP. 51
TRANSFORM ANALYSIS OF SYSTEMS
The frequency response of a type I linear phase filter may be expressed in the form
where
Type I1 Linear Phase Filters
A type I1 linear phase filter has a symmetric unit sample response, and N is odd. Therefore, the center of symmetry of h ( n ) occurs at the halfinteger value a, = N / 2 , as illustrated in Fig. 53(b). The frequency response of a type I1 linear phase filter may be written as where
Type 111 Linear Phase Filters
A type I11 linear phase filter has a unit sample response that is antisymmetric, and N is even. Therefore, h ( n ) is antisymmetric about a = N / 2 , which is an integer, as illustrated in Fig. 53(c). The frequency response of a type 111 linear phase filter may be written as where
'Qpe 1V Linear Phase Filters
A type IV linear phase filter has a unit sample response that is antisymmetric, and N is odd. Therefore, h ( n ) is antisymmetric about the halfinteger value a = N / 2 , and the frequency response has the form where
The zWansform of Linear Phase Systems
The symmetries in the unit sample response of a linear phase system impose constraints on the system function H ( z ) . For a type I or I1 filter, h ( n ) = h ( N  n ) , which implies that

