Smoothing 1D not equidistant curve by convolution

The filtering is done with a triangle filter by convolution of the resampled non equidistant curve. Also with automatic filter generation.

Smoothing 1D not equidistant curve by convolution

The filtering is done with a triangle filter by convolution of the resampled non equidistant curve. Also with automatic generation of suitable filter width.

In order to get a full curve filtering, the curve is linear extrapolated on both sides and not zero padded.

1 Manual

Invoke the function with: [ys,wout*,xse*,yse*]=smooth1DconvNE(xy,w*)

*) optional arguments

Valid is also e.g.: ys =smooth1DconvNE(xy)

1.1 Input:

The first argument xy is the curve to be smoothed.

The first column contains the x-values and the second column contains the corresponding y-values. The input xy may be also crated as two rows. The minimum are 3 sample pairs.

The 2nd argument, called w (width of filter), is optional.

w is a scalar floating number in x-units. 0 ≤ w < 0.9 * length of curve.

For w=0 no filtering, but a resampled curve xse, yse is returned.

Two modes are possible:

1.) w omitted: Filter width is determined by FFT.

2.) w is set as a floating number in x-units and used as filter.

1.2 Output:

ys: smoothed y as vertical vector. The x-values remain unchanged. Vertical vector.

wout: filter width used

xse: resampled equidistant x-values of the smoothed curve. Vertical vector.

yse: resampled equidistant y-values of the smoothed curve. Vertical vector.

In case of a bad input, all outputs are set to zero.

1.3 Remark:

The border values of the smoothed output ys are approximations. In order to calculate those values, the input y is extended by extrapolation of the smoothed input. The approximated border output is one half of the filter width.