barcode print in asp net Fig. 1-15 ( a ) Continuous-time system; ( b )discrete-time system. in .NET

Maker Denso QR Bar Code in .NET Fig. 1-15 ( a ) Continuous-time system; ( b )discrete-time system.

Fig. 1-15 ( a ) Continuous-time system; ( b )discrete-time system.
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C Systems with Memory and without Memory .
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A system is said to be memoryless if the output at any time depends on only the input at that same time. Otherwise, the system is said to have memory. An example of a memoryless system is a resistor R with the input x ( t ) taken as the current and the voltage taken as the output y ( t ) . The input-output relationship (Ohm's law) of a resistor is
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An example of a system with memory is a capacitor C with the current as the input x( t ) and the voltage as the output y ( 0 ; then
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A second example of a system with memory is a discrete-time system whose input and output sequences are related by
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D. Causal and Noncausal Systems: A system is called causal if its output y ( t ) at an arbitrary time t = t,, depends on only t the input x ( t ) for t I o . That is, the output of a causal system at the present time depends on only the present and/or past values of the input, not on its future values. Thus, in a causal system, it is not possible to obtain an output before an input is applied to the system. A system is called noncausal if it is not causal. Examples of noncausal systems are
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Note that all memoryless systems are causal, but not vice versa.
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SIGNALS AND SYSTEMS
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[CHAP. 1
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E. Linear Systems and Nonlinear Systems:
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If the operator T in Eq. (1.60) satisfies the following two conditions, then T is called a linear operator and the system represented by a linear operator T is called a linear system:
1. Additivity:
Given that Tx, = y , and Tx, for any signals x , and x2.
2. Homogeneity (or Scaling):
= y,,
then
T{x, +x2) = y , +Y,
for any signals x and any scalar a. Any system that does not satisfy Eq. (1.66) and/or Eq. (1.67) is classified as a nonlinear system. Equations (1.66) and ( 1.67) can be combined into a single condition as (1.68) T { ~+ w 2 ) = ~ I Y + a 2 Y z I I where a , and a, are arbitrary scalars. Equation (1.68) is known as the superposition property. Examples of linear systems are the resistor [Eq. (1.6111 and the capacitor [Eq. ( 1.62)]. Examples of nonlinear systems are (1.69) y =x2
y = cos x
(1.70)
Note that a consequence of the homogeneity (or scaling) property [Eq. (1.6711 of linear systems is that a zero input yields a zero output. This follows readily by setting a = 0 in Eq. (1.67). This is another important property of linear systems.
Time-Invariant and Time-Varying Systems: A system is called rime-inuariant if a time shift (delay or advance) in the input signal causes the same time shift in the output signal. Thus, for a continuous-time system, the system is time-invariant if for any real value of shift-incariant ) if
For a discrete-time system, the system is time-invariant (or ~ { x [ -n ] ) = y [ n - k ] k (1.72)
for any integer k . A system which does not satisfy Eq. (1.71) (continuous-time system) or Eq. (1.72) (discrete-time system) is called a time-varying system. To check a system for time-invariance, we can compare the shifted output with the output produced by the shifted input (Probs. 1.33 to 1.39).
Linear Time-Invariant Systems
If the system is linear and also time-invariant, then it is called a linear rime-invariant (LTI) system.
CHAP. 1 1
SIGNALS AND SYSTEMS
H. Stable Systems:
A system is bounded-input/bounded-output (BIBO) stable if for any bounded input x defined by
the corresponding output y is also bounded defined by
where k , and k, are finite real constants. Note that there are many other definitions of stability. (See Chap. 7.)
I. Feedback Systems:
A special class of systems of great importance consists of systems having feedback. In a feedback system, the output signal is fed back and added to the input to the system as shown in Fig. 1-16.
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