![]() ![]() We see that the step response s( t) is just the running integral of the impulse response h( t). H( t - τ) = 0, t - τ 0, is the system BIBO stable? How about for a < 0? Let's examine the convolution equation, flipping h( t) instead of x( t): We know that h( t) is the system response toĪnother way to look at the causality condition: In other words, a response to an input at t = t 0, would occur only for t t 0 and not before t 0. ![]() We know that for a causal system, the output depends only on past or present inputs and not on future inputs.Įquivalently, a causal system does not respond to an input until it occurs (the output is not based on the future). We will see how to do this when we study transforms. For this to hold, the system must be one-to-one. It must be constant or else the system wouldįor y( t)= K x( t), the impulse response h( t) must be of the form of a unit impulse weighted by a constant K:Ī system is invertible if we can find h I( t) so that the original input x( t) can be recovered from the output y( t). It does not depend on either past or future inputs.Īn LTI system that is memoryless can only have this form: In a memoryless system, the output y( t) is a function of the 3.1 Example 4 Poles and Stability 5 Poles and Eigenvalues 6 Transfer Functions Revisited 7. Of conditions on the impulse response h( t). 1 Stability 2 BIBO Stability 3 Determining BIBO Stability. In this section, we will express other known system attributes in terms Y( t) = x( t) * h( t), that is, the output of the system is simply the convolution of the input with the system's impulse response. Properties of an LTI system are completely determined by If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded. BIBO stands for Bounded-Input Bounded-Output. ![]() Properties of Continuous-Time LTI systems In signal processing, specifically control theory, BIBO stability is a form of stability for linear signals and systems that take inputs. ![]()
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