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| + | == Part C. Linearity == | ||
| + | If, for any two inputs, x1(t) and x2(t), you can apply each to a system to produce y1(t) and y2(t) respectively, then multiply each y(t) by a constant complex number, called a and b respectively, then add ay1(t)+by2(t) to produce a final output z(t). Then, if you again take x1(t) and x2(t), but this time first multiply each by a and b respectively, where a and b are again constant complex numbers, then add ax1(t)+bx2(t) and apply this input to the system to get an output w(t). If z(t)=w(t), then this system can be called a linear system. | ||
| + | == Example of a Linear System == | ||
| + | Suppose a system produces the output y(t)=2x(t-1) | ||
Revision as of 11:07, 11 September 2008
Part C. Linearity
If, for any two inputs, x1(t) and x2(t), you can apply each to a system to produce y1(t) and y2(t) respectively, then multiply each y(t) by a constant complex number, called a and b respectively, then add ay1(t)+by2(t) to produce a final output z(t). Then, if you again take x1(t) and x2(t), but this time first multiply each by a and b respectively, where a and b are again constant complex numbers, then add ax1(t)+bx2(t) and apply this input to the system to get an output w(t). If z(t)=w(t), then this system can be called a linear system.
Example of a Linear System
Suppose a system produces the output y(t)=2x(t-1)
