barcode lib ssrs w, = tan 2 in Software

Encoder Code 128B in Software w, = tan 2

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 tifth-order type I Chebyshev
Code-128 Creator In Visual Studio .NET
Using Barcode creation for ASP.NET Control to generate, create Code128 image in ASP.NET applications.
Code-128 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 discrete-time 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).
UPC-A Supplement 5 Generator In None
Using Barcode drawer for Software Control to generate, create UPC-A image in Software applications.
Generating EAN 13 In None
Using Barcode encoder for Software Control to generate, create EAN-13 Supplement 5 image in Software applications.
FILTER DESIGN
Code 39 Full ASCII Creator In None
Using Barcode creation for Software Control to generate, create Code-39 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 discrete-time Chebyshev high-pass filter with an equiripple passband with
Paint EAN-13 In .NET Framework
Using Barcode printer for Reporting Service Control to generate, create EAN-13 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 Code-128 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 discrete-time high-pass filter, there are two approaches that we may use. We may design an analog type I Chebyshev low-pass filter, map it into a Chebyshev low-pass filter using the bilinear transformation, and then perform a low-pass-to-high-pass transformation in the z-domain. Alternatively, before applying the bilinear transformation. we could perform a low-pass-to-high-pass transformation in the s-plane and then map the analog high-pass filter into a discrete-time high-pass 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 high-pass 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 continuous-time domain. With T, = 2 and W R = tan -
Using the transformation s -+ I 1s to map these high-pass filter cutoff frequencies to low-pass 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 second-order Chebyshev filter we should come close to meeting the specifications. Therefore, we will use N = 2. The next step is to design a second-order low-pass Chebyshev filter with
where C!, = 1.9627 and R , = 6.3 138. With
CHAP. 91 it follows that
FILTER DESIGN
For a second-order Chebyshev filter, we need to generate a second-order 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 left-half s-plane are at
Thus, the second-order Chebyshev filter is
Now we transform this low-pass filter into a high-pass filter with the low-pass-to-high-pass 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
2-l)'
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 low-pass 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 low-pass 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 )
i-2. = tan
i-2.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,
Copyright © OnBarcode.com . All rights reserved.