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barcode lib ssrs Fig. 98. Frequency response of Chebyshev type I filter for orders N = 5 and N = 6. in Software
Fig. 98. Frequency response of Chebyshev type I filter for orders N = 5 and N = 6. Reading Code 128B In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code128 Generation In None Using Barcode maker for Software Control to generate, create Code 128 Code Set B image in Software applications. The system function of a type I Chebyshev filter has the form
Code 128 Code Set B Decoder In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Code 128 Drawer In C#.NET Using Barcode generation for Visual Studio .NET Control to generate, create Code 128 Code Set B image in VS .NET applications. where H,(O) = ( 1  c2)'I2 if N is even, and H,(O) = 1 if N is odd. Given the passband and stopband cutoff frequencies, Q , and Q,, and the passband and stopband ripples, 8 , and 6, (or the parameters E and A), the steps involved in designing a type I Chebyshev filter are as follows: Find the values for the selectivity factor, k, and the discrimination factor, d. Determine the filter order using the formula Encoding Code 128C In Visual Studio .NET Using Barcode drawer for ASP.NET Control to generate, create Code128 image in ASP.NET applications. Code 128C Encoder In .NET Framework Using Barcode encoder for VS .NET Control to generate, create Code 128A image in .NET framework applications. Form the rational function
USS Code 128 Generator In Visual Basic .NET Using Barcode creator for .NET Control to generate, create Code128 image in .NET framework applications. Creating Data Matrix ECC200 In None Using Barcode creator for Software Control to generate, create Data Matrix 2d barcode image in Software applications. , where E = [(l  s , )  ~ 1 1 l / ~ and construct the system function H,(s) by taking the N poles of G,(s) that lie in the lefthalf splane. Print EAN 128 In None Using Barcode encoder for Software Control to generate, create EAN / UCC  14 image in Software applications. Drawing GS1  13 In None Using Barcode creator for Software Control to generate, create UPC  13 image in Software applications. EXAMPLE 9.4.2 If we were to design a lowpass type I Chebyshev filter to meet the specificationsgiven in Example 9.4.1 where we found d = 0.0487 and k = 0.6, the required filter order would be Code 128 Code Set B Generator In None Using Barcode generation for Software Control to generate, create Code 128 image in Software applications. Painting Barcode In None Using Barcode drawer for Software Control to generate, create barcode image in Software applications. or N = 4. Therefore, with
Identcode Creator In None Using Barcode maker for Software Control to generate, create Identcode image in Software applications. Bar Code Creator In Java Using Barcode encoder for Java Control to generate, create bar code image in Java applications. and then where 52, = 2n(6000). Scanning Code 3 Of 9 In C# Using Barcode decoder for .NET framework Control to read, scan read, scan image in .NET framework applications. Decode Code 3/9 In VB.NET Using Barcode decoder for VS .NET Control to read, scan read, scan image in VS .NET applications. FILTER DESIGN
Bar Code Generator In VB.NET Using Barcode generator for Visual Studio .NET Control to generate, create barcode image in Visual Studio .NET applications. Drawing Code39 In None Using Barcode drawer for Microsoft Word Control to generate, create Code39 image in Microsoft Word applications. [CHAP. 9
Printing Code 128 Code Set B In .NET Using Barcode maker for .NET Control to generate, create Code 128A image in VS .NET applications. GTIN  128 Generation In ObjectiveC Using Barcode printer for iPad Control to generate, create EAN128 image in iPad applications. A type I1 Chebyshev filter, unlike a type 1 filter, has a monotonic passband and an equiripple stopband, and the system function has both poles and zeros. The magnitude of the frequency response is where N is the order of the filter, 52, is the passband cutoff frequency, R, is the stopband cutoff frequency, and E is the parameter that controls the stopband ripple amplitude. Again, as the order N is increased. the number of ripples increases and the transition width becomes narrower. Examples are given in Fig. 99 for N = 5 , 6 . ( b ) Even order (N = 6). (a)Odd order (N = 5). Fig. 99. Frequency response of a Chebyshev type I1 filter for orders N = 5 and N = 6. The system function of a type I1 Chebyshev filter has the form
The poles are located at
Q ak = Sk
where sk for k = 0, I, . . . , N  1 are the poles of a type 1 Chebyshev filter. The zeros bk lie on the j52axis at the frequencies for which TN(Q,/ R ) = 0. The procedure for designing a type 11 Chebyshev filter is the same as for a type I filter, except that = ( 8 .  1) ' I 2 ~ ~ Elliptic Filter
An elliptic filter has a system function with both poles and zeros. The magnitude of its frequency response is where UN(52/Qp) is a Jacobian elliptic function. The Jacobian elliptic function U N ( x ) a rational function of is order N with the following property: Elliptic filters have an equiripple passband and an equiripple stopband. Because the ripples are distributed uniformly across both bands (unlike the Butterworth and Chebyshev filters, which have a monotonically decreasing CHAP. 91
FILTER DESIGN
passband and/or stopband), these filters are optimum in the sense of having the smallest transition width for a given filter order, cutoff frequency Q,, and passband and stopband ripples. The frequency response for a 4thorder elliptic filter is shown in Fig. 9 10. Fig. 910. The magnitude of the frequency response of a sixthorder elliptic filter.
The design of elliptic filters is more difficult than the Butterworth and Chebyshev filters, because their design relies on the use of tables or series expansions. However, the filter order necessary to meet a given set of specifications may be estimated using the formula where d is the discrimination factor, and
where with k being the selectivity factor.
9.4.2 Design of ZZR Filters from AnalogFilters
The design of a digital filter from an analog prototype requires that we transform ha(t) to h(n) or Ha(s) to H(z). A mapping from the splane to the zplane may be written as where s = m(z) is the mapping function. In order for this transformation to produce an acceptable digital filter, the mapping m(z) should have the following properties: The mapping from the jS2axis to the unit circle, Izl = 1, should be one to one and onto the unit circle in order to preserve the frequency response characteristics of the analog filter. 2. Points in the lefthalf splane should map to points inside the unit circle to preserve the stability of the analog filter. 3. The mapping m(z) should be a rational function of z so that a rational Ha(s) is mapped to a rational H(z). Described below are two approaches that are commonly used to map analog filters into digital filters.

