Line 12: Line 12:
 
Ex) What is the output of:
 
Ex) What is the output of:
  
<math> x[n] = e^{j*pi*n}  ->  n*e^{-j*pi*n} </math>
+
<math> x[n] = e^{j*\pi*n}  ->  n*e^{-j*\pi*n} </math>
  
 
<math> x[n] \to Sys 1 \to n*x[-n] </math>
 
<math> x[n] \to Sys 1 \to n*x[-n] </math>
Line 18: Line 18:
  
 
from:
 
from:
<math> e^{j*n*y} = cos(n*y) + j*sin(n*y) \pi </math>
+
<math> e^{j*n*y} = cos(n*y) + j*sin(n*y) </math>
  
 
we determine:
 
we determine:
 
x[n] = cos(
 
x[n] = cos(

Revision as of 14:26, 18 September 2008

The Basics of Linearity

A system is linear if its inputs are sequentially equal to the outputs for a certain function:

$ x(t) = a*x1(t) + b*x2(t) = a*y1(t) + b*y2(t) $


Take for a simple example:

Ex) What is the output of:

$ x[n] = e^{j*\pi*n} -> n*e^{-j*\pi*n} $

$ x[n] \to Sys 1 \to n*x[-n] $


from: $ e^{j*n*y} = cos(n*y) + j*sin(n*y) $

we determine: x[n] = cos(

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