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USS128 Printer In Java Using Barcode creation for Java Control to generate, create UCC.EAN  128 image in Java applications. Paint Code 128 In None Using Barcode generator for Microsoft Word Control to generate, create Code 128 Code Set A image in Microsoft Word applications. Evaluate the weighted error function over the set . by interpolating between the extremal frequencies F using the Lagrange interpolation formula. Select a new sel of extremal frequencies by choosing the L error function is maximum. UPCA Supplement 2 Drawer In Visual Studio .NET Using Barcode drawer for Reporting Service Control to generate, create GTIN  12 image in Reporting Service applications. Printing Barcode In ObjectiveC Using Barcode creator for iPhone Control to generate, create barcode image in iPhone applications. + 2 frequencies for which the interpolated
If the extremal frequencies have changed, repeat the iteration from step 2.
A design formula that may be used to estimate the equiripple filter order for a lowpass filter with a transition width Af , passband ripple 6,. and stopband ripple 6 , is EXAMPLE 9 3 3 Suppose thal we would like to design an equiripple lowpass filter with a passband cutoff frequency .. w,, = 0 . 3 ~a. stopband cutoff frequency o,= 0 . 3 5 ~a, passband ripple of 6, = 0.01, and a stopband ripple of 6, = 0.001. Estimating the filter using Eq. (9.h),we find Because we want the ripple in Ihe stopband to be I0 times smaller than the ripple in the passband, the error must be weighted usmg the weighting function Using the ParksMcClellan algorilhm to design the filter. we obtain a filter with the frequency response magnitude shown below. 9.4 IIR FILTER DESIGN There are two general approaches used to design IIR digital filters. The most common is to design an analog IIR filter and then map it into an equivalent digital filter because the art of analog filter design is highly advanced. Therefore, it is prudent to consider optimal ways for mapping these filters into the discretetime domain. Furthermore, because there are powerful design procedures that facilitate the design of analog filters, this approach CHAP. 91
FILTER DESIGN
to IIR filter design is relatively simple. The second approach to design IIR digital filters is to use an algorithmic design procedure, which generally requires the use of a computer to solve a set of linear or nonlinear equations. These methods may be used to design digital filters with arbitrary frequency response characteristics for which no analog filter prototype exists or to design filters when other types of constraints are imposed on the design. In this section, we consider the approach of mapping analog filters into digital filters. Initially, the focus will be on the design of digital lowpass filters from analog lowpass filters. Techniques for transforming these designs into more general frequency selective filters will then be discussed. 9.4.1 Analog LowPass Filter Prototypes
To design an IIR digital lowpass filter from an analog lowpass filter, we must first know how to design an analog lowpass filter. Historically, most analog filter approximation methods were developed for the design of passive systems having a gain less than or equal to 1. Therefore, a typical set of specifications for these filters is as shown in Fig. 95(a),with the passband specifications having the form ((I) Specifications in terms of
and 6,. ( I ) Specifications in terms of e and A.
Fig. 95. Tivo different conventions for specifying the passband and stopband deviations for an analog lowpass filter. Another convention that is commonly used is to describe the passband and stopband constraints in terms of the parameters E and A as illustrated in Fig. 95(h). Two auxiliary parameters of interest are the dist.riminatior7 factor, and the selectivity factor
k =" The three most commonly used analog lowpass filters are the Butterworth, Chebyshev, and elliptic filters. These filters are described below.

