MATLAB SIGNAL PROCESSING BLOCKSET 7 Guide de l'utilisateur télécharger pdf (Page 418)

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Least Squares Polynomial Fit

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5Least Squares Polynomial Fit

Purpose Compute the coefficients of the polynomial that best fits the input data in a

least-squares sense.

Library Math Functions / Polynomial Functions

Description The Least Squares Polynomial Fit block computes the coefficients of the nth

order polynomial that best fits the input data in the least-squares sense, where

n is specified by the

Polynomial order parameter. A distinct set of n+1

coefficients is computed for each column of the M-by-N input, u.

For a given input column, the block computes the set of coefficients,

, c

,…,c

n+1

, that minimizes the quantity

where u

is the ith element in the input column, and

The values of the independent variable, x

, x

,…,x

, are specified as a

length-M vector by the

Control points parameter. The same M control points

are used for all N polynomial fits, and can be equally or unequally spaced. The

equivalent MATLAB code is shown below.

c = polyfit(x,u,n) % Equivalent MATLAB code

Inputs can be frame-based or sample-based. For convenience, a length-M 1-D

vector input is treated as an M-by-1 matrix.

Each column of the (n+1)-by-N output matrix, c, represents a set of n+1

coefficients describing the best-fit polynomial for the corresponding column of

the input. The coefficients in each column are arranged in order of descending

exponents, c

, c

,…,c

n+1

. The output is always sample-based.

Example In the model below, the Polynomial Evaluation block uses the second-order

polynomial

–()

i 1=

∑

() c

n 1–

L c

n 1+

+++==

y 2– u

3+=

1 2 ... 413 414 415 416 417 418 419 420 421 422 423 ... 737 738

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MATLAB SIGNAL PROCESSING BLOCKSET 7 Guide de l'utilisateur Page 418

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