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CH2.doc
The response of a continuous-time LTI system can be computed by convolution of the impulse response of the system with the input signal, using a convolution integral, rather than a sum.
LTI System
Long-term behavior in a system is predicted using LTI systems. The term "linear translation-invariant" can be used to describe these systems, giving it the broadest meaning possible.
The initial no energy storage of an lti system
The zero-input response, which is what the system does with no input at all. This is due to initial conditions, such as energy stored in capacitors and inductors. The zero-state response, which is the
module1-2_LTI_AT
Since most periodic (non-periodic) signals can be decomposed into a summation (integration) of sinusoids via Fourier Series (Transform), the response of a LTI system to virtually any input is
The LTI system is said to be initially relaxed system when
An LTI system is "initially relaxed" or "at rest" if all its initial conditions are zero before an input is applied. This means there is no stored energy in the system.
Linear time-invariant system
Any system that can be modeled as a linear differential equation with constant coefficients is an LTI system. Examples of such systems are electrical circuits made up of resistors, inductors, and
PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS
If a discrete-time LTI system has an impulse response h[n] that is not identically zero for n ± 0, then the system has memory. An example of an LTI system with memory is the system given by eq. (2.42).
Linear Systems I Lecture 3
Def. (relaxed system): A system is said to be relaxed at t0 if its initial state x(t0) is 0. In this case the output y(t), t > t0 is excited exclusively by the input u(t) for t > t0.
State Variable Description of LTI systems
Set of variables of smallest possible size that together with any input to the system is sufficient to determine the future behavior (I.e., output) of the system.
It is known that an lti system has no energy storage initially
For LTI systems, these two concepts capture the same essential property of dynamical systems, that is, a system with this property does not generate its own energy but only stores and dissipates
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