LTI SYSTEM PROPERTIES
LTI SYSTEM PROPERTIES AND THE IMPULSE RESPONSE
The impulse response completely characterizes the LTI system. Here, we will discuss system properties such as memory, causality, stability and invertibility related to impulse response of LTI system.
LTI systems with and without memory
A system is memoryless if its output at any time depends only on the value of the input at the same time. The output of a discrete-time system
Causality for LTI system
The output of a causal system depends only on the present and past values of the input.
The convolution sum
Stability of LTI system
A system is stable if every bounded input results in bounded output.
Let x[n] be bounded in magnitude
Invertibility of LTI system
Consider a continuous-time LTI system with impulse response h(t). This system is invertible only if an inverse system exists that, when connected in series with the original system, produces an output equal to the input to the first system
STEP RESPONSE OF AN LTI SYSTEM
The unit step response s(t) or s[n] is response corresponding to unit step that is x(t)= u(t) or x[n] = u[n]
The unit step response can also be used to characterize an LTI system, since we can calculate the impulse response from it.
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