18-07-2014, 12:45 PM
Signals and Systems
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. Introduction to Signals
A signal is a function of one or more independent variables. It can
be, for example, a voltage or an image. In our discussion, a signal is
considered as a function of time. However, we should realize that the
addressed theory may also apply to other cases.
A continuous-time signal, also called an analog signal, is defined
along a continuum of time. An example of continuous-time signals is
. Introduction to Systems
A system is a device which converts an input signal into an output
signal. The input signal is also called excitation and the output signal
is also called response.
A continuous-time system is a system whose input and output are
continuous-time signals (figure 1.4). A discrete-time system is a
system whose input and output are discrete-time signals (figure 1.5).
A continuous-time system may be implemented by a discrete-time
system (figure 1.6). A discrete-time system may be implemented by a
continuous-time system
. Memoryless Systems versus Systems with Memory
A system is memoryless if the output at any time depends only on
the input at the same time. Otherwise, the system has memory.
Example. Determine whether system y(n)=x(nn0
), where n0 is an
integer, is memoryless.1.3.4. Causal Systems versus Noncausal Systems
A system is causal if the output at any time depends only on the
input at and before this time. Otherwise, the system is noncausal.
A noncausal system cannot be implemented in real time.
Example. Determine whether the following systems are causal:
Invertible Systems versus Noninvertible Systems
System A is invertible if system B exists such that when A and B
are cascaded, the output of B is equal to the input of A (figures 1.8
and 1.9). B is referred to as the inverse system of A. Otherwise, A is
noninvertible.
There exists a one-to-one correspondence between the input and
the output of an invertible system: (1) For a given input, the output
can be determined uniquely. Actually, both invertible systems and
noninvertible systems satisfy this condition. (2) For a given output,
the input can be determined uniquely. Only invertible systems satisfy
this condition