Spline interpolation introduces negative values

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Wed, 07/30/2014 - 06:08 pm

I have a number of waves, strictly positive, of 2049 points. I do an interpolation down to 100 points:

Interpolate2/T=3/N=100/I=2/F=0/Y=spec_VT095_n_SS/X=freq_VT095_SS freq_VT095, spec_VT095_n

(spec=spectrum, freq=frequency).

The interpolation introduces some negative values in the new wave. What is the reason for this, and how can I overcome it?

A test experiment is attached. Experiment_6.pxp
The cubic spline, and the smoothing spline, fit a local cubic polynomial to sets of contiguous points. What you see is the result of those fits. There is no reason for the output values to be non-negative - they just need to satisfy the cubic polynomial equation which is different for each set of points.

Since your data has an abrupt change over few points at the beginning, you get what you see.

Smoothing spline interpolation has no analytical value - it is just to produce a smooth curve for visual effect. It works best noisy but reasonably smooth input.

If you set the first point to NaN and then redo the smoothing spline, you get better results because you have removed the discontinuity from the input:

Variable saveFirstPoint = spec_VT095_n[0]
spec_VT095_n[0] = NaN
Interpolate2/T=3/N=100/I=2/F=0/Y=spec_VT095_n_SS/X=freq_VT095_SS freq_VT095, spec_VT095_n
spec_VT095_n[0] = saveFirstPoint



Here is a recreation macro for the graph I used to examine the data:
Window Graph0() : Graph
    PauseUpdate; Silent 1       // building window...
    Display /W=(12,51,1038,674) spec_VT095_n vs freq_VT095
    AppendToGraph spec_VT095_n_SS vs freq_VT095_SS
    ModifyGraph mode(spec_VT095_n)=3
    ModifyGraph marker(spec_VT095_n)=19
    ModifyGraph rgb(spec_VT095_n_SS)=(1,16019,65535)
    SetAxis left -4.40425531914894e-08,5.55957446808511e-07
    SetAxis bottom -0.00941051769868653,0.16067755017735
    Cursor/P A spec_VT095_n 3
    ShowInfo
EndMacro

July 30, 2014 at 06:56 pm - Permalink

Thanks. I see your point. I was expecting that the noisiness is responsible for this behavior, but was not sure.

Thanks again.

July 31, 2014 at 08:56 am - Permalink