Smoothing by Least Square Technique !!!

Hi all,

We are trying to find coefficients ' a 's for a given 200x1 t and 200x1 r(t)

r(t) = [ 1530 1215 3243 1111 ..... ]' size: 200 x 1

t = [0:0.5:99.5] size: 200 x 1

N=200

Thanks :)

Answer 1

[Star Strider]

Interesting problem. The system is essentially this matrix equation:

r = A*[t^n]

where r, t and n are defined by necessity as column vectors and A is the matrix of coefficients. This is the inverse of the usual least-squares problem:

t = 0:0.5:99.5;                 % Define ‘t’
n = 0:length(t)-1;              % Define ‘n’
tn = t.^n;                      % Define ‘t^n’
r = [1530 1215 3243 1111]';     % Given ‘r’ vector

stn = tn(1:length(r))';         % Truncate length of ‘tv’ to match sample ‘r’
stn(1) = eps;                   % Replace zero with ‘eps’ in ‘stv’

stni = pinv(stn);               % Take pseudo-inverse of ‘t^n’

A = r*stni                      % Calculate ‘A’ coefficient matrix

rt = A*stn                      % Verify ‘A’ calculation

At least for the data available, this works!

Answer 2

[Image Analyst]

See my attached demo for polyfit.

[Serhat]

In your code, you give constant values for slope,intercept etc.

But, we dont have these values. We want to find the polynomial coeffcients which best fits the our original data. We just have the data vectors.

Thanks

[Image Analyst]

I did not give constants for them. I computed all the coefficients (slope and intercept). Look again, specifically for these lines where I calculate them:

% Do the regression with polyfit
linearCoefficients = polyfit(x, y, 1)