Line 17: Line 17:
  
  
<math> e^{j*n*y} = cos(n*y) + j*sin(n*y) </math>
+
from:
 +
<math> e^{j*n*y} = cos(n*y) + j*sin(n*y) \pi </math>
 +
 
 +
we determine:
 +
x[n] = cos(

Revision as of 15:25, 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) \pi $

we determine: x[n] = cos(

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