Define and give an example for each of the following concepts in the context of signals and systems:

i) A stable system

ii) A time-varying system

i) A stable system is a system whose output remains bounded for all possible bounded inputs. In other words, if the input to a stable system is bounded, then the output of the system will also be bounded. Stability is a fundamental property of systems, as it ensures that the system behaves predictably and does not produce unbounded or unpredictable responses.

One example of a stable system is a simple low-pass filter, which attenuates high-frequency components of an input signal. The transfer function of a low-pass filter is given by H(s) = 1 / (1 + RCs), where R and C are the resistor and capacitor values, respectively, and s is the Laplace variable. This transfer function is stable for any positive values of R and C. If the input to the filter is a ________ _______ __________ ___ _________ _____ _______ ____ ___ _________ ___ ____.
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