(New page: == Definition == A system in which the outputs are components of an linear eqation which is equal to the value of a linear operator applied to a linear equation whose components are the i...) |
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A system in which the outputs are components of an linear eqation which is equal to the value of a linear operator applied to a linear equation whose components are the inputs. | A system in which the outputs are components of an linear eqation which is equal to the value of a linear operator applied to a linear equation whose components are the inputs. | ||
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| + | == Examples == | ||
| + | |||
| + | Linear System: | ||
| + | |||
| + | <font size="2">Equation: <math>y[n] = 54x[n]</math></font> | ||
| + | |||
| + | <math>x_{1}[n] \to sys \to *a \to</math> | ||
| + | <math>+ \to 54a x_{1}[n] + 54b x_{2}[n]</math> | ||
| + | <math>x_{2}[n] \to sys \to *b \to</math> | ||
| + | |||
| + | <math>x_{1}[n] \to *a \to</math> | ||
| + | <math>+ \to sys \to 54a x_{1}[n] + 54b x_{2}[n]</math> | ||
| + | <math>x_{2}[n] \to *b \to</math> | ||
| + | |||
| + | Non-Linear System: | ||
| + | |||
| + | <font size="2">Equation: <math>y[n] = x[n]^4</math></font> | ||
| + | |||
| + | <math>x_{1}[n] \to sys \to *a \to</math> | ||
| + | <math>+ \to a x_{1}[n]^4 + b x_{2}[n]^4</math> | ||
| + | <math>x_{2}[n] \to sys \to *b \to</math> | ||
| + | |||
| + | <math>x_{1}[n] \to *a \to</math> | ||
| + | <math>+ \to sys \to (a x_{1}[n] + b x_{2}[n])^4</math> | ||
| + | <math>x_{2}[n] \to *b \to</math> | ||
Latest revision as of 13:28, 10 September 2008
Definition
A system in which the outputs are components of an linear eqation which is equal to the value of a linear operator applied to a linear equation whose components are the inputs.
Examples
Linear System:
Equation: $ y[n] = 54x[n] $
$ x_{1}[n] \to sys \to *a \to $ $ + \to 54a x_{1}[n] + 54b x_{2}[n] $ $ x_{2}[n] \to sys \to *b \to $
$ x_{1}[n] \to *a \to $ $ + \to sys \to 54a x_{1}[n] + 54b x_{2}[n] $ $ x_{2}[n] \to *b \to $
Non-Linear System:
Equation: $ y[n] = x[n]^4 $
$ x_{1}[n] \to sys \to *a \to $ $ + \to a x_{1}[n]^4 + b x_{2}[n]^4 $ $ x_{2}[n] \to sys \to *b \to $
$ x_{1}[n] \to *a \to $ $ + \to sys \to (a x_{1}[n] + b x_{2}[n])^4 $ $ x_{2}[n] \to *b \to $
