(New page: == Linearity == So a system is linear if its inputs x1(t), x2(t) or (x1[n], x2[n] for Discrete Time signals) yield outputs y1(t), y2(t) such as the response: a*x1(t)+b*x2(t) => a*y1(t)+b...) |
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== Linearity == | == Linearity == | ||
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x1[n] -> [sys] -> y1[n]=2*x1[n]^3 -> (X)*a +++ | x1[n] -> [sys] -> y1[n]=2*x1[n]^3 -> (X)*a +++ | ||
| − | + | = a*2*x1[n]^3+2*b*x2[n]^3 | |
x2[n] -> [sys] -> y2[n]=2*x2[n]^3 -> (X)*b +++ | x2[n] -> [sys] -> y2[n]=2*x2[n]^3 -> (X)*b +++ | ||
Revision as of 08:07, 12 September 2008
Linearity
So a system is linear if its inputs x1(t), x2(t) or (x1[n], x2[n] for Discrete Time signals) yield outputs y1(t), y2(t) such as the response: a*x1(t)+b*x2(t) => a*y1(t)+b*y2(t).
Example: Linear
Example: Non-Linear
y[n] = 2*x[n]^3
x1[n] -> [sys] -> y1[n]=2*x1[n]^3 -> (X)*a +++
= a*2*x1[n]^3+2*b*x2[n]^3
x2[n] -> [sys] -> y2[n]=2*x2[n]^3 -> (X)*b +++
