06-04-2012, 11:48 AM
Analysis of LTI – CT Systems
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Impulse response
. The response of an LTI system due to an
impulse input.
• denoted by h(t)
Convolution integral
• Let x(t) be an arbitrary input applied to
the system H.
• response from the system is denoted as
y(t)
Causality & Stability
Using Impulse response h(t) of the
systems , Causality and Stability are
defined as follows
Causality: For system to be causal, then
Transfer Function
• Let the Laplace transform of x(t) be X(s) and the
Laplace of the output y(t) be Y(s). Now the
transfer function of the system is defined as the
ratio of Y(s) to X(s) when the initial conditions
are zero. It is denoted by H(s).
Frequency Response
• Let the Fourier transform of x(t) be X(jw) and the
Fourier of the output y(t) be Y(jw). Now the
frequency response of the system is given by the
ratio of Y(j w) to X(jw) when the initial conditions
are zero. It is denoted by H(j w).