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barcode print in asp net Fig. 53 Relationships between inputs and outputs in an LTI system. in .NET framework
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Code 3/9 Generation In Java Using Barcode printer for BIRT reports Control to generate, create USS Code 39 image in BIRT reports applications. UPCA 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 continuoustime 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. 54(a) and ( b ) .Taking the Fourier transform of both sides of Eq. (5.791, we get Y ( t) = q
Y ( o )= Kejw'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 (= Keju'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. 54(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. 54 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 continuoustime LTI systems of practical interest are described by linear constantcoefficient 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 timedifferentiation 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 continuoustime 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 frequencyselective behavior. Ideal FrequencySelective Filters: An ideal frequencyselective 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 frequencyselective filters are the following. 1. Ideal LowPass Filter:

