barcode reading in asp.net Ck = 1 Ti2 g(f)e -jkw,tdt T I -TR in Software

Painting Code 128 in Software Ck = 1 Ti2 g(f)e -jkw,tdt T I -TR

Ck = 1 Ti2 g(f)e -jkw,tdt T I -TR
Read USS Code 128 In None
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
Generating USS Code 128 In None
Using Barcode drawer for Software Control to generate, create Code-128 image in Software applications.
Applying this to i(t), the sequence of unit impulses given by EQ. (22.3)) one obtains
Code 128 Code Set A Decoder In None
Using Barcode decoder for Software Control to read, scan read, scan image in Software applications.
Code 128C Creator In Visual C#
Using Barcode creator for .NET framework Control to generate, create Code 128 Code Set C image in .NET framework applications.
i(t) = 1 Ckejkosr kc-CO
Code 128B Maker In Visual Studio .NET
Using Barcode printer for ASP.NET Control to generate, create Code 128B image in ASP.NET applications.
Generating Code 128 In .NET Framework
Using Barcode creator for VS .NET Control to generate, create Code 128 Code Set A image in .NET applications.
where
Encoding Code 128 In VB.NET
Using Barcode encoder for .NET Control to generate, create Code-128 image in .NET framework applications.
Bar Code Drawer In None
Using Barcode drawer for Software Control to generate, create barcode image in Software applications.
s(t - nT)e-jkWstdt
Code 128 Code Set B Creation In None
Using Barcode encoder for Software Control to generate, create ANSI/AIM Code 128 image in Software applications.
GS1 128 Generation In None
Using Barcode drawer for Software Control to generate, create UCC.EAN - 128 image in Software applications.
In the range of integration from -T/2 to T/2, the only term in the summation of delayed unit-impulse functions that contributes to the integrand is s(t); therefore, we may write the equation for Ck as
Generate GS1 - 13 In None
Using Barcode printer for Software Control to generate, create GS1 - 13 image in Software applications.
Code 39 Extended Creator In None
Using Barcode generation for Software Control to generate, create Code 39 image in Software applications.
W)e -ik%tdt
Painting ANSI/AIM Codabar In None
Using Barcode creator for Software Control to generate, create USS Codabar image in Software applications.
USS Code 39 Generator In Java
Using Barcode generation for Java Control to generate, create Code 3 of 9 image in Java applications.
One can show that this integral becomes 1; therefore
Making UPC - 13 In .NET
Using Barcode printer for Visual Studio .NET Control to generate, create EAN 13 image in .NET framework applications.
Data Matrix Generator In None
Using Barcode generation for Font Control to generate, create ECC200 image in Font applications.
ck = f
Barcode Printer In Java
Using Barcode generator for Android Control to generate, create bar code image in Android applications.
Generating Code39 In VS .NET
Using Barcode generation for VS .NET Control to generate, create Code 3/9 image in .NET framework applications.
Equation (22.4) can now be written
Make UPC Symbol In None
Using Barcode maker for Online Control to generate, create UCC - 12 image in Online applications.
EAN / UCC - 13 Drawer In Java
Using Barcode generator for Android Control to generate, create UCC.EAN - 128 image in Android applications.
f*(t) = f(t); 2 ejkost k=-cc
SAMPLING
Z-TRANSFORMS
After placing f(t) inside the summation, we take the Laplace transform of each side of the above equation and apply the theorem on the translation of a transform from Chap. 4 to each term on the right side; the result is F*(s) = LCf*(t)} = f 2 F(s + jko,) kc-m Use will be made of this expression in the next chapter. (22.9)
CHAPTER
OPEN-LOOP AND CLOSED-LOOP RESPONSE
To calculate the open-loop response of a sampled-data system, one can develop a pulse transfer function that is the counterpart of the transfer function for continuous systems.
OPEN-LOOP RESPONSE Pulse Tkansfer Function
Consider the block diagram in Fig. 23.1 in which an impulse-modulated signal enters a block having the transfer function G(s). We may write C(s) = G(s)F*(s) (23.1)
Let there be a fictitious sampler attached to the output of G(s). Using the alternate definition for a starred transform from the previous chapter [Eq. (22.9)], the sampled function C*(S) in Fig. 23.1 may be written:
C*(s) = f 5 C(s + jnw,) = f f: G(s + jnms)F*(s + jno,) (23.2) n=-a n=-co
As shown in the appendix of this chapter, F*(s) is periodic in s with frequency w,, which means that
F*(s) = F*(s + jno,) (23.3)
OPFN-LOOP
AND CLOSED-LOOP RESPONSE
Fictitious sampler 2 b--d
c*(f) r-c (4
C(z)
FIGURE 23-1
Open-loop sampled-data system.
Equation (23.2) may be written: (23.4) C*(s) = F*(s) $ 2 G(s + jno,) n=-CO 1 I Recognizing the term within braces on the right side to be simply G *(s) according to the alternate definition of the starred transform given by Eq. (22.9), we may write (23.5) C*(s) = F*(s)G*(s) Recalling that the Z-transform is simply the Laplace transform of the starred function in which z 7 eTs , Eq. (23.5) may be written (23.6) C(z) = Ftz)Gtz) The term G(z) is called the pulse trunsfer function. Equation (23.6) states that the sampled output is equal to the product of the sampled input and the pulse transfer function. This is analogous to the continuous case where we write C(S) = F(s)G(s). Note that the inverse of C(z) gives information about c(t) only at sampling instants, 0, T, 2T, 3T, . . . ,nT.
Example 23.1. Use of the pulse transk function. To see how Eq. (23.6) may be used, consider the example shown in Fig. 23.2 in which a triangular wave signal enters the sampler. For this example
G(s) = & = -
l/T S+$
(23.7)
From a table of Z-transforms (Table 22.1) we obtain for this G(s) G(z) = i, _ ,+
(23.8)
FIGURE 23-2
Example of an open-loop system.
SAMPLED-DATA CONTROL SYSTEMS
Using the basic definition of a Z-transform in Eq. (22.8), we may express the output of the sampler as: F(z) = -j f(nT)z- = 0 + z-l +2z-*+z-3+o
(23.9)
Applying Eq. (23.6) gives
c(~) =
F(z)G(z) = (z-l + 2z-* + z- )
(23.10)
or 1 1+ 22-1 + 2-2 C(z) = ; z - e-Tf~ For the purpose of having a numerical result, let T = 1 and T = 1. Then T/r = 1 and emT/ = 0.368. The problem now facing us is the inversion of Eq. (23.11). Ike methods will be discussed: (1) long division and (2) use of a table of Z-transforms. To apply the method of long division, we simply divide the denominator of Eq. (23.11) into its numerator as shown here. z-l + 2.368z-* + 1.871~-~ + .** z - 0.368 I 1 1 + 2z- +
- 0.368z- 2.368z- 2.368z- + Z-* - 0.871z-* 1.8712-2
From this result, we may write C(z) = z-l + 2.368z-* + 1.871~-~ + *** (23.12) Interpretation of Eq. (23.12) in the time domain may be done with the aid of the basic definition of the Z-transform of Eq. (22.8) by recognizing the coefficients of the terms on the right side of Eq. (23.12) to be the values of c(t) at sampling instants; thus c(O) = 0 c(T) = 1.0
c(2T) = 2.368 c(3T) = 1.871
and so on Recall that the inversion of the Z-transform gives information about the continuous function c(t) only at sampling instants. The values of c(t) at times other than sampling instants must be obtained by some other means. Later, we shall show that the modified Z-transform can be used to obtain intersample information. One may also apply basic knowledge of the response of the system to determine c(t) at times between sampling instants. For a first-order response, this
Copyright © OnBarcode.com . All rights reserved.