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iFit/smooth

PURPOSE ^

Z = smooth(Y) : smooth iData objects

SYNOPSIS ^

function b = smooth(a, varargin)

DESCRIPTION ^

 Z = smooth(Y) : smooth iData objects

   @iData/smooth function to smooth iData objects
     The smooth method uses a Robust spline smoothing or Savitzky-Golay algorithm
     The spline smoothing relies on a frequency spline smoothing (discrete cosine
     transform), whereas the Savitzky-Golay uses a generalized moving average 
     with filter coefficients determined by an unweighted linear least-squares 
     regression and a polynomial model of specified degree (default is 2).
     The spline method is shape preserving, whereas the Savitzky-Golay may lead
     to important distribution modifications.

   Z = SMOOTH(Y) automatically smoothes the uniformly-sampled array Y. Y
   can be any N-D noisy array (time series, images, 3D data,...). Non
   finite data (NaN or Inf) are treated as missing values.

   Z = SMOOTH(Y,S) smoothes the data Y using the smoothing parameter S.
   S must be a real positive scalar. The larger S is, the smoother the
   output will be. If the smoothing parameter S is omitted (see previous
   option) or empty (i.e. S = []), it is automatically determined using
   the generalized cross-validation (GCV) method.

   Z = SMOOTH(Y,W) or Z = SMOOTH(Y,W,S) specifies a weighting array W of
   real positive values, that must have the same size as Y. Note that a
   nil weight corresponds to a missing value.

   Z = SMOOTH(Y,'sgolay') uses the Savitzky-Golay method (2nd order)
   Z = SMOOTH(Y,'sgolay',degree) uses the Savitzky-Golay method with polynomial 
   degree specified by degree.
   Z = SMOOTH(Y,span,'sgolay',degree) uses the number of data points specified 
   by span in the Savitzky-Golay calculation. span must be odd and degree must 
   be less than span.
   Z = SMOOTH(Y,span,'sgolay',degree,dimensions) specifies the dimensions along
   which the Savitzky-Golay filter should be applied (integer or vector up to ndims).

   Z = SMOOTH(Y, 'gauss', [ widths ]) uses a nD gaussian convolution

   Robust smoothing
   ----------------
   Z = SMOOTHN(...,'robust') carries out a robust smoothing that minimizes
   the influence of outlying data.

   Reference
   --------- 
   Garcia D, Robust smoothing of gridded data in one and higher dimensions
   with missing values. Computational Statistics & Data Analysis, 2010. 
   <a href="matlab:web('http://www.biomecardio.com/pageshtm/publi/csda10.pdf')">PDF download</a>
   http://www.biomecardio.com/matlab/smoothn.html

   Numerical recipes in C. p 650

 input:  a: object or array (iData/array of)
 output: s: smoothed data set (iData)
 ex:     c=smooth(a);

 Version: Mar. 22, 2017
 See also iData, iData/interp

CROSS-REFERENCE INFORMATION ^

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