Re: detrend

[Teemu Ikonen]

On Wed, 18 Oct 2000, flatmax wrote:

> Can any one technically define what is happening in the 'detrend'
> algorithm ?
> 
> function y = detrend (x, p)
>   r = rows (x);
>   b = ((1 : r)' * ones (1, p + 1)) .^ (ones (r, 1) * (0 : p));
>   y = x - b * (b ŠÜ x);

The second row creates a polynomial fitting matrix (Vandermonde
matrix) b. b could also be written as 
[(1:r)'.^0, (1:r)'.^1, ..., (1:r)'.^p]

In the third row (b ŠÜ x) is a solution (in least squares sense) to 
b*a = x,
where vector a has length p+1. b*a (= b * (b ŠÜ x)) is then simply a vector
of values of the best fit polynomial of order p to data x. This is then
subtracted from the original data.

HTH,

Teemu



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