barcode print in asp net Fig. 5-3 Relationships between inputs and outputs in an LTI system. in .NET framework

Drawing Denso QR Bar Code in .NET framework Fig. 5-3 Relationships between inputs and outputs in an LTI system.

Fig. 5-3 Relationships between inputs and outputs in an LTI system.
Denso QR Bar Code Recognizer In .NET Framework
Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in .NET applications.
Painting QR Code In .NET Framework
Using Barcode creation for .NET framework Control to generate, create QR image in .NET applications.
Consider the complex exponential signal with Fourier transform (Prob. 5.23) X(w) = 2 d q w - 0,) Then from Eqs. (5.66) and ( I .26) we have Y(o)
QR Code 2d Barcode Scanner In .NET
Using Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in .NET applications.
Bar Code Generation In Visual Studio .NET
Using Barcode generation for Visual Studio .NET Control to generate, create bar code image in .NET framework applications.
= 27rH(wo) 6(w
Barcode Reader In .NET
Using Barcode decoder for .NET framework Control to read, scan read, scan image in .NET applications.
QR Code ISO/IEC18004 Generator In C#.NET
Using Barcode encoder for .NET Control to generate, create QR Code image in VS .NET applications.
- too)
Making Denso QR Bar Code In .NET
Using Barcode encoder for ASP.NET Control to generate, create QR Code JIS X 0510 image in ASP.NET applications.
QR Code Generation In VB.NET
Using Barcode generator for Visual Studio .NET Control to generate, create QR Code image in VS .NET applications.
Taking the inverse Fourier transform of Y(w), we obtain y(f ) = H(wo) eioll' which indicates that the complex exponential signal ei"l)' is an eigenfunction of the LTI system with corresponding eigenvalue H(w,), as previously observed in Chap. 2 (Sec. 2.4 and Prob. 2.171. Furthermore, by the linearity property (5.491, if the input x ( t ) is periodic with the Fourier series ~ ( 1= )
USS Code 39 Encoder In .NET
Using Barcode drawer for .NET framework Control to generate, create Code 3 of 9 image in .NET applications.
EAN 128 Generation In Visual Studio .NET
Using Barcode creation for .NET Control to generate, create EAN / UCC - 14 image in .NET applications.
&= -m
Barcode Creator In .NET Framework
Using Barcode creator for .NET framework Control to generate, create barcode image in VS .NET applications.
Code 93 Full ASCII Creator In VS .NET
Using Barcode encoder for .NET Control to generate, create USS 93 image in .NET framework applications.
ckejkw,+
Generate Bar Code In .NET Framework
Using Barcode generator for ASP.NET Control to generate, create barcode image in ASP.NET applications.
Create Code 128 Code Set B In None
Using Barcode creator for Software Control to generate, create Code 128 Code Set C image in Software applications.
(5.73)
Make Barcode In Java
Using Barcode maker for Java Control to generate, create barcode image in Java applications.
Drawing European Article Number 13 In Objective-C
Using Barcode creator for iPad Control to generate, create EAN / UCC - 13 image in iPad applications.
then the corresponding output y(l) is also periodic with the Fourier series
Make 1D In Visual C#.NET
Using Barcode generator for VS .NET Control to generate, create Linear 1D Barcode image in VS .NET applications.
Creating Code-128 In None
Using Barcode maker for Office Word Control to generate, create Code128 image in Office Word applications.
CHAP. 51
Code 3/9 Generation In Java
Using Barcode printer for BIRT reports Control to generate, create USS Code 39 image in BIRT reports applications.
UPC-A Supplement 2 Creation In None
Using Barcode creation for Online Control to generate, create GTIN - 12 image in Online applications.
FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS
If x ( t ) is not periodic, then from Eq. (5.30)
and using Eq. (5.66), the corresponding output y ( t ) can be expressed as
Thus, the behavior of a continuous-time LTI system in the frequency domain is completely characterized by its frequency response H(w 1. Let
X ( w ) = IX(o)leiexcw)
Then from Eq. (5.66) we have
Y ( o )= lY(w)leiey(o)
(5.77) (5.78a) (5.78b)
b'(o)l= IX(w)llH(o)l
e y ( 4 =e
x b >+ e ~ b ) Hence, the magnitude spectrum IX(o)( of the input is multiplied by the magnitude response JH(w)l the system to determine the magnitude spectrum JY(w)lof the output, of and the phase response O,(o) is added to the phase spectrum O,(w) of the input to of produce the phase spectrum Oy(o) the output. The magnitude response IH(o)l is sometimes referred to as the gain of the system.
B. Distortionless Transmission:
For distortionless transmission through an LTI system we require that the exact input signal shape be reproduced at the output although its amplitude may be different and it may be delayed in time. Therefore, if x ( t ) is the input signal, the required output is
(5.79) t - t,) where t, is the time delay and K ( > 0)is a gain constant. This is illustrated in Figs. 5-4(a) and ( b ) .Taking the Fourier transform of both sides of Eq. (5.791, we get
Y ( t) = q
Y ( o )= Ke-jw'dX(w) H ( w )= I
Thus,
(5.80) (5.81)
Thus, from Eq. (5.66) we see that for distortionless transmission the system must have
H ( ~ ) ~ ~ ~ ~ H (= Ke-ju'd W)
That is, the amplitude of H ( o ) must be constant over the entire frequency range, and the phase of H ( w ) must be linear with the frequency. This is illustrated in Figs. 5-4(c)and ( d l .
Amplitude Distortion and Phase Distortion:
When the amplitude spectrum IH(o)( of the system is not constant within the frequency band of interest, the frequency components of the input signal are transmitted with a different amount of gain or attenuation. This effect is called amplitude distortion. When the phase spectrum OH(w) the system is not linear with the frequency, the output of
FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS
[CHAP. 5
' I +Id
Fig. 5-4 Distortionless transmission.
signal has a different waveform than the input signal because of different delays in passing through the system for different frequency components of the input signal. This form of distortion is called phase distortion.
C. LTI Systems Characterized by Differential Equations:
As discussed in Sec. 2.5, many continuous-time LTI systems of practical interest are described by linear constant-coefficient differential equations of the form
with M I N . Taking the Fourier transform of both sides of Eq. (5.83) and using the linearity property (5.49) and the time-differentiation property (5.551, we have
CHAP. 51
FOURIER ANALYSIS O F TIME SIGNALS AND SYSTEMS
Thus, from Eq. (5.67)
which is a rational function of o.The result (5.85) is the same as the Laplace transform counterpart H ( s ) = Y(s)/X(s) with s = jo [Eq. (3.40)], that is,
5.6 FILTERING
One of the most basic operations in any signal processing system is filtering. Filtering is the process by which the relative amplitudes of the frequency components in a signal are changed or perhaps some frequency components are suppressed. As we saw in the preceding section, for continuous-time LTI systems, the spectrum of the output is that of the input multiplied by the frequency response of the system. Therefore, an LTI system acts as a filter on the input signal. Here the word "filter" is used to denote a system that exhibits some sort of frequency-selective behavior.
Ideal Frequency-Selective Filters:
An ideal frequency-selective filter is one that exactly passes signals at one set of frequencies and completely rejects the rest. The band of frequencies passed by the filter is referred to as the pass band, and the band of frequencies rejected by the filter is called the stop band. The most common types of ideal frequency-selective filters are the following.
1. Ideal Low-Pass Filter:
Copyright © OnBarcode.com . All rights reserved.