 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
barcode lib ssrs I Transformation I in Software
I Transformation I Code 128 Recognizer In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Generating Code 128 Code Set B In None Using Barcode generator for Software Control to generate, create Code128 image in Software applications. Mapping
Decoding Code 128 In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Code128 Creator In C# Using Barcode generator for .NET framework Control to generate, create Code 128 Code Set A image in Visual Studio .NET applications. New Cutoff Frequencies
Code128 Printer In .NET Using Barcode maker for ASP.NET Control to generate, create Code 128 Code Set C image in ASP.NET applications. Code128 Generator In VS .NET Using Barcode creation for Visual Studio .NET Control to generate, create Code 128A image in .NET applications. The second approach that may be used is to design an analog lowpass filter, map it into a digital filter using a suitable splane to zplane mapping, and then apply an appropriate frequency transformation in the discretetime domain to produce the desired frequency selective digital filter. Table 96 provides a list of some digitaltodigital transformations. The two approaches do not always result in the same design. For example, although the second approach could be used to design a highpass filter using the impulse invariance technique, with the first approach the design would be unacceptable due to the aliasing that would occur when sampling the analog highpass filter. Code128 Drawer In VB.NET Using Barcode generation for .NET Control to generate, create Code128 image in .NET applications. Encode GS1  12 In None Using Barcode creation for Software Control to generate, create GTIN  12 image in Software applications. FILTER DESIGN BASED ON A LEAST SQUARES APPROACH
Making Bar Code In None Using Barcode drawer for Software Control to generate, create bar code image in Software applications. Encode EAN / UCC  13 In None Using Barcode creation for Software Control to generate, create EAN / UCC  13 image in Software applications. The design techniques described in the previous section are based on converting an analog filter into a digital filter. It is also possible to perform the design directly in the time domain without any reference to an analog filter. This section describes several methods for designing a digital filter directly. Making ANSI/AIM Code 128 In None Using Barcode creator for Software Control to generate, create Code 128B image in Software applications. ANSI/AIM Code 39 Drawer In None Using Barcode creator for Software Control to generate, create ANSI/AIM Code 39 image in Software applications. CHAP. 91
Leitcode Generator In None Using Barcode printer for Software Control to generate, create Leitcode image in Software applications. Print GS1128 In None Using Barcode generator for Font Control to generate, create EAN / UCC  13 image in Font applications. FILTER DESIGN
Bar Code Recognizer In Visual Basic .NET Using Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in Visual Studio .NET applications. Paint UCC.EAN  128 In Java Using Barcode generation for Android Control to generate, create EAN / UCC  13 image in Android applications. Table 96 The Transformation of a Digital LowPass Filter with a Cutoff Frequency w, to Other Frequency Selective Filters GTIN  13 Generator In Java Using Barcode creator for Java Control to generate, create EAN / UCC  13 image in Java applications. Recognize Code 3 Of 9 In Visual Basic .NET Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications. Filter Type Lowpass Mapping
ANSI/AIM Code 128 Creation In VB.NET Using Barcode drawer for .NET Control to generate, create Code 128B image in .NET framework applications. Painting UPC Code In None Using Barcode creation for Font Control to generate, create UPC Code image in Font applications. Design Parameters sin[(w,.  w:.)/2] sinl(w,. q ' . ) / 2 ] w:. = desired cutoff frequency
Highpass
2' + cr ul
cos[(w,. w:.)/21 cos[(w,  w3/21 w: = desired cutoff frequency
Bandpass
wCl= desired lower cutoff frequency = desired upper cutoff frequency
Bandstop
w,,~= desired lower cutoff frequency w,2 = desired upper cutoff frequency
9.5.1 Pad4 Approximation
Let h d ( n )be the unit sample response of an ideal filter that is to be approximated by a causal filter that has a unit sample response, h ( n ) ,and a rational system function, Because H ( z ) has p q 1 free parameters, it is generally possible to find values for the coefficients a ( k ) and h(k) so that h ( n ) = h d ( n )for n = 0, 1 , . . . , p q . The procedure that is used to find these coefficients is to write H ( z ) = B ( z ) / A ( z )as follows, and note that, in the time domain, the lefthand side corresponds to a convolution
(note that b(n) is a finitelength sequence that is equal to zero for n .c0 and n z q). Setting h ( n ) = hd(n)for n = 0 1, . . . , p q results in a set of p q + 1 linear equations in p q + 1 unknowns, . hd(n) + &o(k)hd(n
~ = I
k ) = n = 0. I . . . . , q {E(n) n=q+l, ...,q+p
FILTER DESIGN
[CHAP. 9
that may be solved using a twostep approach. In the first step, the coefficients a ( k ) are found using the last p equations in Eq. (9.14),which may be written in matrix form as Assuming that these equations are linearly independent, the coefficients may be uniquely determined. In the second step, the coefficients b ( k ) are found from the first 9 1 equations in Eq. (9.14) as follows: Although PadC's method produces an exact match of h ( n ) to h d ( n )for n = 0. 1. . . . , p 9, because h ( n ) is unconstrained for n > p q , the PadC method does not generally produce a good approximation to h d ( n )for n > p+q. 9.5.2 Prony ' Method s
With a leastsquares approach to filter design, the problem is to find the coefficients a ( k ) and b ( k )that minimize the leastsquares error where U is some preselected upper limit. Because E is a nonlinear function of the coefficients a ( k ) and b(k), solving this minimization problem is, in general, difficult. With Prony's method, however, an approximate leastsquares solution may be found using a twostep procedure as follows. Ideally, because [see Eq. (9.14)] the first step is to find the coefficients a ( k ) that minimize
where Once the coefficients a ( k ) have been determined, the coefficients h ( k ) are found using the PadC approach of' forcing h ( n ) = h d ( n )for n = 0, 1. . . . , 9 : The coefficients a ( k ) that minimize E may be found by setting the partial derivatives of E equal to zero,

