 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
barcode lib ssrs CHAP. 91 in Software
CHAP. 91 Code 128 Code Set B Scanner In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code128 Drawer In None Using Barcode generation for Software Control to generate, create Code 128 Code Set A image in Software applications. FILTER DESIGN
Decoding USS Code 128 In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Generate Code 128 Code Set B In C#.NET Using Barcode generation for .NET Control to generate, create Code 128 image in .NET applications. (a) The bilinear transformation is defined by the mapping
Encoding USS Code 128 In VS .NET Using Barcode drawer for ASP.NET Control to generate, create Code 128 Code Set B image in ASP.NET applications. ANSI/AIM Code 128 Printer In Visual Studio .NET Using Barcode drawer for .NET framework Control to generate, create Code 128B image in .NET framework applications. Therefore, for the given filter, we have
Encode Code 128 Code Set B In Visual Basic .NET Using Barcode creator for .NET Control to generate, create USS Code 128 image in .NET applications. Draw ECC200 In None Using Barcode generator for Software Control to generate, create Data Matrix 2d barcode image in Software applications. which has poles at
European Article Number 13 Encoder In None Using Barcode encoder for Software Control to generate, create EAN13 image in Software applications. Bar Code Generation In None Using Barcode generation for Software Control to generate, create bar code image in Software applications. z2 = Ih To find the zeros, it is necessary to combine the two terms in the system function over a common denominator. Doing this. we have GTIN  12 Creator In None Using Barcode creation for Software Control to generate, create UPCA image in Software applications. Drawing EAN / UCC  13 In None Using Barcode printer for Software Control to generate, create GS1 128 image in Software applications. zl =
ISBN  13 Maker In None Using Barcode printer for Software Control to generate, create International Standard Book Number image in Software applications. Generating GS1 DataBar Expanded In Java Using Barcode printer for Java Control to generate, create DataBar image in Java applications. I I a
EAN13 Scanner In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Creating Barcode In None Using Barcode drawer for Font Control to generate, create barcode image in Font applications. Finding the roots of the numerator may be facilitated by noting that H,(s) has a zero at s = co,which gets mapped to z =  1 with the bilinear transformation. Therefore. one of the factors of the numerator is ( 1 zI). Dividing the numerator by this factor, we obtain the second factor, which is [(2  a  b)  2z'1. Thus, H ( ; ) has zeros at Generating Barcode In Visual Basic .NET Using Barcode creation for .NET framework Control to generate, create barcode image in .NET framework applications. Generating Data Matrix 2d Barcode In Java Using Barcode creation for Java Control to generate, create DataMatrix image in Java applications. (b) With the impulse invariance technique, for firstorder poles, the mapping is
Universal Product Code Version A Generation In C# Using Barcode drawer for .NET framework Control to generate, create UPC Symbol image in .NET applications. GS1  12 Recognizer In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. Therefore, with T, = 2 we have
which has two poles at
z1=eL1
and only one zero. which is located at
z:!=e2h
z,, = i(e2" + eZb
The system function of a digital fi lter is
(a) If this filter was designed using impulse invariance with T, = 2, find the system function, H&), of an analog filter that could have been the analog filter prototype. Is your answer unique (b) Repeat part (a) assuming that the bilinear transformation was used with T, = 2. (a) Because H ( z ) is expanded in a partial fraction expansion, the poles at z = a k in H ( z ) are mapped from poles in Ha(s)according to the mapping ( y k = esl Therefore, if T, = 2, sk =
FILTER DESIGN
and one possible analog filter prototype is
[CHAP. 9
Because the mapping from the splane to the zplane is not one to one, this answer is not unique. Specifically, note that we may also write = @rT,+iZn
Therefore, with T, = 2, we may also have
and another possible analog Rlter prototype is
(6) With the bilinear transformation, because the mapping from the splane to the zplane is a onetoone mapping, with T, = 2, I +s z=I S and the analog filter prototype that is mapped to H ( z ) is unique and given by A continuoustime system is called an inlegrator. if the response of the system y,(r) to an input x u ( [ )is The system function for an integrator is
( a ) Design a discretetime "integrator" using the bilinear transformation, and find the difference equation relating the input x ( n ) to the output y ( n ) of the discretetime system. (b) Find the frequency response of the discretetime integrator found in part ( a ) ,and determine whether or not this system is a good approximation to the continuoustime system. (a) With a system function H&) = I/s, the bilinear transformation produces a discretetime filter with a system function The unit sample response of this filter is
and the difference equation relating the output y ( n ) to the input s ( n ) is
CHAP. 91
FILTER DESIGN
(b) Because the frequency response of the continuoustime system, H,(jR) = I / j R , is related to the discretetime filter through the mapping
the frequency response of the discretetime system is
Note that because H (ejC") to zero at w = n ,then H ( e J wwill not be a good approximation to H,(jR) = goes ) 1 / j R except for low frequencies. However, if w < I, using the expansion < sinxxx
x<<1
we have and we have, for the frequency response.
Therefore, for small w
H (ciw)% T,H,(jR) Let H,(jQ) be an Nthorder lowpass Butterworth filter with a 3dB cutoff frequency Q,. (a) Show that H,(s) may be transformed into an Nthorder highpass Butterworth filter by adding N zeros at s = 0 and scaling the gain. ( 6 ) What is the relationship between the corresponding digital lowpass and highpass Butterworth filters that are designed using the bilinear transformation (a) For an N thorder lowpass Butterworth with a system function H,(s), Adding N zeros to H,(s) at s = 0, we have
Multiplying numerator and denominator by ( J R , yields
which corresponds to a magnitudesquared frequency response
by Scaling t f u ( j R ) RN results in a filter that has a frequency response G , ( j R )with a squared magnitude which is a highpass filter with a cutoff frequency R,.. Specifically, note that IC,(jR)12 is equal to zero at R = 0, and that I C , ( ~ R+ ~ ~ R + oo, ) 1 as FILTER DESIGN
[CHAP. 9
( h ) Applying the bilinear transformation to a lowpass Butterworth filter, we have
For the highpass filter, on the other hand, we have
Therefore, we see that the poles of the lowpass digital Butterworlh filter are the same as those of the highpass digital Butterworth filter. The zeros, however, which are at z =  I in the case of the lowpass filter, are at z = I in the highpass filter. Thus, excepl for a difference in the gain, the highpass digital Butterworth filter may be derived from the lowpass filler by flipping the N zeros in H ( z ) at z =  1 to z = 1. The impulse invariance method and the bilinear transformation are two filter design techniques that preserve stability of the analog filter by mapping poles in the lefthalf splane to poles inside the unit circle in the zplane. An analog filter is minimum phase if all of its poles and zeros are in the lefthalf splane. ( a ) Determine whether or not a minimum phase analog tilter is mapped to a minimum phase discretetime system using the impulse invariance method.

