Smoothing of arbitrary 1D curves

Smoothing of curves that are not equal spaced sampled and with not monotonic ascending x values

Smooth1D_NE_NM

Smoothing of arbitrary 1D curves.

Curves that are not equal spaced sampled and with not monotonic ascending x values.

1 Manual

1.1 Input

The first argument xy is a n x 2 or 2 x n array with the x and y values, n>3.

It must contain numeric values, no NaN

Example: xy = [ 4, 6;

2, 8;

-10, -5;

4, 6 ];

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

Two modes are possible:

1.) w omitted: Moving triangle auto width filter.

Filter width is automatically determined by the length of the curve

Example: [xes,yes,wout]=smooth1D_NE_NM(xy)

2.) w is set as floating number >0. w is the filter width as length:

0 < w < 0.9 * (length of noisy curve)

Example: [xes,yes,wout]=smooth1DconvNE(xy, 6.7)

1.2 Output

xes: x values of smoothed xy

yes: y values of smoothed xy

wout: filter width used. This may be a little different to the w set by user.

1.3 Error

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

2 Method

The steps for smoothing are:

• Parametrize the noisy curve to x(S) and y(S), S is cumulative curve length
• Define a filter
• Extrapolate curve at both ends with a little more than the half filter width
• Resample the noisy curve including extrapolation
• Filter xe(Se) and ye(Se) by convolution

For more details read the enclosed pdf.