 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
barcode lib ssrs FILTER DESIGN in Software
FILTER DESIGN Code 128B Scanner In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Printing ANSI/AIM Code 128 In None Using Barcode drawer for Software Control to generate, create Code 128 image in Software applications. [CHAP. 9
Read Code 128B In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. Printing Code 128 Code Set A In Visual C#.NET Using Barcode encoder for Visual Studio .NET Control to generate, create Code128 image in .NET applications. Use the impulse invariance method to design a digital filter from an analog prototype that has a system function Code 128A Creator In Visual Studio .NET Using Barcode creation for ASP.NET Control to generate, create ANSI/AIM Code 128 image in ASP.NET applications. Drawing Code 128 Code Set C In VS .NET Using Barcode generator for VS .NET Control to generate, create Code 128 Code Set C image in VS .NET applications. Ha(s) = Create Code128 In Visual Basic .NET Using Barcode encoder for .NET Control to generate, create Code128 image in .NET framework applications. Create Code 39 Extended In None Using Barcode creation for Software Control to generate, create Code 39 image in Software applications. + + h2
Make EAN / UCC  14 In None Using Barcode generator for Software Control to generate, create GTIN  128 image in Software applications. UPCA Supplement 5 Maker In None Using Barcode generator for Software Control to generate, create UPCA image in Software applications. + (a + jh) Data Matrix ECC200 Generation In None Using Barcode drawer for Software Control to generate, create ECC200 image in Software applications. Generate Code 128B In None Using Barcode maker for Software Control to generate, create Code128 image in Software applications. To design a filter using the impulse invariance technique, we first expand H,,(s) in a partial fraction expansion as follows, UPCE Printer In None Using Barcode drawer for Software Control to generate, create GTIN  12 image in Software applications. Read Code 128 Code Set B In Visual Studio .NET Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET applications. HAS)= Create Matrix Barcode In .NET Using Barcode encoder for ASP.NET Control to generate, create Matrix Barcode image in ASP.NET applications. Encoding Code 128A In Visual Studio .NET Using Barcode printer for Reporting Service Control to generate, create Code 128 Code Set C image in Reporting Service applications. + + b2
Data Matrix 2d Barcode Recognizer In C#.NET Using Barcode recognizer for VS .NET Control to read, scan read, scan image in .NET applications. Code128 Printer In ObjectiveC Using Barcode creator for iPhone Control to generate, create ANSI/AIM Code 128 image in iPhone applications. ~ 1 ) ~
Bar Code Scanner In .NET Using Barcode reader for .NET Control to read, scan read, scan image in Visual Studio .NET applications. Bar Code Creation In ObjectiveC Using Barcode creator for iPhone Control to generate, create bar code image in iPhone applications. + (a  jb) where
and Therefore, with
Hu(s)= s+a+,jh+s+a using the mapping given in Eq. (9.10), we have
cos(bT,). Thus, the location of the zero in the discreteNote that the zero at s = a is mapped to a zero at z = PT7 time filter depends on the position of the poles as well as the zero in the analog filter. With the impulse invariance method, the unit sample response of a digital filter is formed by sampling the impulse response of the continuoustime filter, Another approach is to use the step invariance method in which the step response of the digital filter is formed by sampling the step response of the continuoustime filter. ( a ) Design a digital filter with the step invariance method using the continuoustime prototype
(6) Determine whether or not the filter is the same as that which would be designed using the impulse invariance method.
( a ) If the impulse response of a continuoustime filter is h,(r), its step response is
Therefore, because the Laplace transform of the step response is related to the system function H,(s) as follows, then
CHAP. 91
FILTER DESIGN
To design a digital filter using step invariance, we first perform a partial fraction expansion of S,(s), where
Therefore. Sampling s,,(t), a I S,, (s) =  a2
a + j h a jh + b2 s + 2(a2+ h2)(s+ u + j h ) + 2(a2 + b2)(s+ a
s ( n ) = s,(nT,) and finding the ztransform of s(n) corresponds to the substitution
Thus, the ztransform of the step response is
The system function of the digital filter is then
( b ) Using impulse invariance, we see from Prob. 9.36 that the system function is
Note that although H ( z ) has the same poles as the filter designed using step invariance, the system functions are not the same. Therefore, the two designs are not equivalent. Suppose that we would like to design a discretetime lowpass filter by applying the impulse invariance method to a continuoustime Butterworth tilter that has a magnitudesquared function FILTER DESIGN The specifications for the discretetime ti lter are
[CHAP. 9
Show that the design is not affected by the value of the sampling period that is used in the impulse invariance technique. In the absence of aliasing, the impulse invariance method is a linear mapping from H,,(jQ) to H(eJL" for Iwl 5 n. This mapping is H W " ) = H,,(;w "! = ,, IwI 5 n Let us assume that there is no aliasing (this will be approximately true if the filter order is large enough). The required filter order is then log d N Z log k where d, the discrimination factor, is (I d = [  6,J2  6;z1 k' = R
and k , the selectivity factor, is Q, Clearly, the discrimination factor does not depend on the sampling period T,. In addition, with w, = Q,T, and w, = Q,T,, it follows that k =  w,,l T,  w,, to,, which does not depend on the sampling period. Therefore, the required filter order is independent of T,. Next, if we expand the system function of the Butterworth filter in a partial fraction expansion. we have where the poles, sk, are
With impulse invariance, the system function of the discretetime filter becomes
and it follows that the poles of H(z) are at
= exp(sl T,) = exp{Q,T,Or
where Because w, = R, T , is the 3dB cutoff frequency of the lowpass filter in the discretetime domain, it is fixed by the tilter specifications. Therefore, the poles of H ( : ) will not be affected by the sampling period T,. For example, if we try to decrease T, to reduce aliasing, this would require an increase in Q, to preserve the cutoff frequency. Thus, 11 follows that the design is not affected by T,. Use the impulse invariance method to design a lowpass digital Butterworth filter to meet the following specifications: CHAP. 91
FILTER DESIGN
In the absence of aliasing, the impulse invariance method is a linear mapping from H,(jR) to H(eJW) Iwl 5 n, for which is given by 5 H(eJ") = ~ . ( . i R ) l ~ , ~ ~ , 1 4 x Therefore, in order to simplify the design, we will assume that there is no aliasing and then, after the design is completed. check to see that the filter satisfies the given specification:;. Because the parameter T, does not enter into the design using the impulse invariance method (see Prob. 9.38), for convenience we will set T, = 1 . The first step, then, is to design an analog Butterworth filter according to the following specifications: To determine the filter order. we compute the discrimination factor,

