13-06-2013, 03:06 PM
Discrete-Time Systems
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A discrete-time system can be thought of as a transformation or operator
that maps an input sequence {x[n]} to an output sequence {y[n]}
Basic System Properties
Systems with or without memory:
A system is said to be memoryless if the out put for each value of the independent
variable at a given time n depends only on the input value at time
n. For example system specified by the relationship
Invertibility
A system is said to be invertible if the input signal {x[n]} can be recovered
from the output signal {y[n]}. For this to be true two different input signals
should produce two different outputs. If some different input signal produce
Time invariance
A system is said to be time invariant if the behavior and characteristics of the
system do not change with time.Thus a system is said to be time invariant
if a time delay or time advance in the input signal leads to identical delay or
advance in the output signal.
Linearity
This is an important property of the system. We will see later that if we
have system which is linear and time invariant then it has a very compact
representation. A linear system possesses the important property of superposition:
if an input consists of weighted sum of several signals, the nthe
output is also weighted sum of the responses of the system to each of those
input signals. Mathematically let {y1[n]} be the response of the system to
the input {x1[n]} and let {y2[n]} be the response of the system to the input
{x2[n]}.