 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
barcode lib ssrs w, = tan 2 in Software
w, = tan 2 Code 128 Code Set C Reader In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code 128 Code Set C Printer In None Using Barcode creation for Software Control to generate, create Code 128 Code Set B image in Software applications. ( ) : Code 128 Decoder In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Drawing Code 128B In Visual C#.NET Using Barcode encoder for Visual Studio .NET Control to generate, create Code 128 image in .NET framework applications. + 1 = 6. and H , , ( s ) is a tifthorder type I Chebyshev
Code128 Creator In Visual Studio .NET Using Barcode creation for ASP.NET Control to generate, create Code128 image in ASP.NET applications. Code128 Creator In .NET Using Barcode creation for .NET Control to generate, create ANSI/AIM Code 128 image in VS .NET applications. Because there are six alternations of I H (eJ'")12in the passband, N filter, Draw Code 128 Code Set A In VB.NET Using Barcode generator for VS .NET Control to generate, create Code 128 Code Set C image in .NET framework applications. ECC200 Printer In None Using Barcode creator for Software Control to generate, create DataMatrix image in Software applications. where A is a constant. Applying the bilinear transformation to HJs) results in a discretetime filter with a system function H(z) that has five poles inside the unit circle, and five zeros on the unit circle at :=  I (as shown in hob. 9.29, the five zeros come from the five zeros in H,,(s) at s = m). UPCA Supplement 5 Generator In None Using Barcode drawer for Software Control to generate, create UPCA image in Software applications. Generating EAN 13 In None Using Barcode encoder for Software Control to generate, create EAN13 Supplement 5 image in Software applications. FILTER DESIGN
Code 39 Full ASCII Creator In None Using Barcode creation for Software Control to generate, create Code39 image in Software applications. Printing EAN 128 In None Using Barcode maker for Software Control to generate, create UCC.EAN  128 image in Software applications. [CHAP. 9
Encode ISBN  13 In None Using Barcode generation for Software Control to generate, create International Standard Book Number image in Software applications. Encoding EAN / UCC  13 In None Using Barcode encoder for Office Excel Control to generate, create EAN 13 image in Microsoft Excel applications. Use the bilinear transformation to design a discretetime Chebyshev highpass filter with an equiripple passband with Paint EAN13 In .NET Framework Using Barcode printer for Reporting Service Control to generate, create EAN13 image in Reporting Service applications. ANSI/AIM Code 39 Creator In Java Using Barcode maker for BIRT Control to generate, create Code 39 image in BIRT reports applications. )0 . 1 USS Code 39 Recognizer In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Paint UCC  12 In Visual C#.NET Using Barcode generator for .NET Control to generate, create UPC Code image in Visual Studio .NET applications. O s w 50.11~ 0.31~ w 5 IT 5
Generating Code 128B In None Using Barcode creation for Online Control to generate, create Code128 image in Online applications. Code 128 Encoder In .NET Using Barcode drawer for Reporting Service Control to generate, create Code128 image in Reporting Service applications. 0.9 5 I H ( & 5 1.0 To design a discretetime highpass filter, there are two approaches that we may use. We may design an analog type I Chebyshev lowpass filter, map it into a Chebyshev lowpass filter using the bilinear transformation, and then perform a lowpasstohighpass transformation in the zdomain. Alternatively, before applying the bilinear transformation. we could perform a lowpasstohighpass transformation in the splane and then map the analog highpass filter into a discretetime highpass filter using the bilinear transformation. Because both methods result in the same design, it does not matter which method we use. Therefore, we will use the second approach, because it is a little easier algebraically. Given that we want lo design a highpass filter with a stopband cutoff frequency ws = 0.117 and a passband cutoff frequency w, = 0.317, we first transform the specifications of the digital filter into the continuoustime domain. With T, = 2 and W R = tan  Using the transformation s + I 1s to map these highpass filter cutoff frequencies to lowpass filter cutoff frequencies, we have and Therefore, the selectivity factor for the analog Chebyshev filter is
With 6, = 6, = 0.1, the discrimination factor is
Thus. the required filter order is
Although we should round up to N = 3, with a secondorder Chebyshev filter we should come close to meeting the specifications. Therefore, we will use N = 2. The next step is to design a secondorder lowpass Chebyshev filter with where C!, = 1.9627 and R , = 6.3 138. With
CHAP. 91 it follows that
FILTER DESIGN
For a secondorder Chebyshev filter, we need to generate a secondorder Chebyshev polynomial. which is Squaring T2(x), we have T;(X) = 4x4  4x2 + I and, for the magnitude squared frequency response of the Chebyshev filter, we have Substituting for the given values of Q, and c, we have
Next, we find H4(s)H4(s) with the substitution St = js, Factoring the denominator polynomial, we find that the two roots in the lefthalf splane are at
Thus, the secondorder Chebyshev filter is
Now we transform this lowpass filter into a highpass filter with the lowpasstohighpass transformations + I /s. This gives Finally, applying the bilinear transformation, we have 3.9778 I
()+ z' I  2' H (z) = + 2.2327(=) + 1
+ 4 . 4 1 8 15+ E ) 2 ( z' Multiplying numerator and denominator by (1 2l)' gives
The magnitude of the frequency response is plotted in the following figure.
FILTER DESIGN
[CHAP. 9
As a check on the design, we may compute the magnitude of the frequency response at w = 0. I n , which is I H ( ~ ~ ~ ) I ~ , 0.1044 , == O , ~
which comes close to satisfying the stopband specifications. At the passband edge, we have
I ~ ( e j ~ ) l , , o . s ,= 0.9044 which does satisfy the constraint.
We would like to design a digital lowpass filter that has a passband cutoff frequency w p = 0 . 3 7 5 ~ with 6, = 0.01 and a stopband cutoff frequency w, = 0.5x with 6 = 0.01. The filter is to be designed using , the bilinear transformation. What order Butterworth, Chebyshev, and elliptic filters are necessary to meet the design specifications To find the required filter order, we begin by finding the discrimination factor and the selectivity factor for the analog lowpass filter prototype. With 8, = 6, = 0.01, the discrimination factor is For the selectivity factor, we first find the cutoff frequencies for the analog prototype. With wp = 0.375r and w, = O S r , we prewarp the frequencies as follows (T, = 2), Rp = tan
0 375r ( = 0.6682 l ) i2. = tan
i2.s
Therefore, R k = 2 = 0.6682  For the Butterworth filter, the required filter order is log d N =   16.25 log k or N = 17. For the Chebyshev filter,

