ANALYSIS OF DISCRETE LINEAR
TIME INVARIANT SYSTEMS
X(n)
system
y(n)
the behavior or response of a linear system to a given input signal
One method is based on the direct
solution of the input-output
equation for the system.
Convolution method
the second method is to decompose the
input signal into a sum of elementary
signals. Then, using the linearity property
of the system, the responses of the system
to the elementary signals are added to
obtain the total response of the system.
The impulse response:
Finite impulse
response
FIR system
system
IIR system
infinite impulse
response
The linear time invariant systems are characterized in the
time domain by their response to a unit sample sequence
an LTI system is causal if and only if its impulse response is zero for negative
values of n.
h(n)
Imp resp is noncausal
and stable
h(n)
Imp resp is causal
and unstable
Various forms of impulse response
h(n)
h(n)
h(n)
Impulse response is
non causal and stable
Impulse response is
causal and stable
Impulse response is
causal and unstable
Example :Find the impulse response of the system described
by the following difference equation y(n)=1.5 y(n-1)-0.85 y(n-2)
+x(n), is this system is FIR or IIR
Thanks for listening