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==Time Invariance== | ==Time Invariance== | ||
A system is called "'''time invariant'''" if for any input signal x(t) in continuous time or x[n] in discrete time and for any time <math>t_0\in{\mathbb R}</math> for continuous time or <math>n_0\in{\mathbb N}</math>, The response to the shifted input <math>x(t-t_{0})</math> or <math>x[n-n_{0}]</math> is the shifted output <math>y(t-t_{0})</math> or <math>y[n-n_{0}]</math> | A system is called "'''time invariant'''" if for any input signal x(t) in continuous time or x[n] in discrete time and for any time <math>t_0\in{\mathbb R}</math> for continuous time or <math>n_0\in{\mathbb N}</math>, The response to the shifted input <math>x(t-t_{0})</math> or <math>x[n-n_{0}]</math> is the shifted output <math>y(t-t_{0})</math> or <math>y[n-n_{0}]</math> | ||
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| + | <math>x(t)\rightarrow system\rightarrow time delay\rightarrow y(t-t_{0})</math> | ||
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| + | <math>x(t)\rightarrow time delay\rightarrow system\rightarrow y(t-t_{0})</math> | ||
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| + | ==Time Variant== | ||
| + | A system is called "'''time variant'''" if for any input signal x(t) in continuous time or x[n] in discrete time and for any time <math>t_0\in{\mathbb R}</math> for continuous time or <math>n_0\in{\mathbb N}</math>, The response to the shifted input <math>x(t-t_{0})</math> or <math>x[n-n_{0}]</math> is not the shifted output <math>y(t-t_{0})</math> or <math>y[n-n_{0}]</math> | ||
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| + | <math>x(t)\rightarrow system\rightarrow time delay\rightarrow y(t-t_{0})</math> | ||
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| + | <math>x(t)\rightarrow time delay\rightarrow system\rightarrow z(t)</math> | ||
Latest revision as of 18:59, 18 September 2008
Time Invariance
A system is called "time invariant" if for any input signal x(t) in continuous time or x[n] in discrete time and for any time $ t_0\in{\mathbb R} $ for continuous time or $ n_0\in{\mathbb N} $, The response to the shifted input $ x(t-t_{0}) $ or $ x[n-n_{0}] $ is the shifted output $ y(t-t_{0}) $ or $ y[n-n_{0}] $
$ x(t)\rightarrow system\rightarrow time delay\rightarrow y(t-t_{0}) $
$ x(t)\rightarrow time delay\rightarrow system\rightarrow y(t-t_{0}) $
Time Variant
A system is called "time variant" if for any input signal x(t) in continuous time or x[n] in discrete time and for any time $ t_0\in{\mathbb R} $ for continuous time or $ n_0\in{\mathbb N} $, The response to the shifted input $ x(t-t_{0}) $ or $ x[n-n_{0}] $ is not the shifted output $ y(t-t_{0}) $ or $ y[n-n_{0}] $
$ x(t)\rightarrow system\rightarrow time delay\rightarrow y(t-t_{0}) $
$ x(t)\rightarrow time delay\rightarrow system\rightarrow z(t) $
