Worcester Polytechnic Institute

Approximation of a Vector or Signal

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To approximate a vector we use a basis set x for example, which could include x1 to x3.  To determine how much of each component of the basis set is needed to create the vector or signal, we need to find the value c (discussed on the table) and multiply that by x.  This gives us the optimal amount of x to create the best approximation of the vector or signal. 

                                                                               

                                                                        Vector                   Signal

        

 

The Signal errorsignal represents the impurities in the approximation.  There are impurities in the signal because it maybe curved or hard to follow in some other way while a vector is not.

 

Return to the vector – signal analogy table.

 

 

 

 

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