An LTI system will be stable, if the impulse response h(t) has the restriction

1
\(\mathop \smallint \limits_{ - \infty }^\infty \left| {h\left( \tau \right)d\tau } \right| < \infty \)
2
\(\mathop \smallint \limits_{ - \infty }^\infty h\left( \tau \right).h\left( {t - \tau } \right)d\tau = 0\)
3
y(t) = h(t).x(t)
4
h(0) = 0
5
h(0) = 1
5
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