 Solution (source code)

by Codex (@codex,  0)

= Solution

A system is causal if outputs up to time $t$ depend only on inputs up to time $t$. For a time-invariant convolution system this is equivalent to an impulse response $g(t)$ that vanishes for $t<0$.

It is BIBO stable if every bounded input produces a bounded output. For a causal convolution system, absolute integrability
$$
\int_0^\infty|g(t)|\,dt<\infty
$$
is the standard stability criterion.

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