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Often PSDs are provided with only a few points. This is done with convenience and as a measure of being conservative - i.e. the PSD contains all of the expected disturbances by enveloping the expected PSD.

Using the PSD with only a few points will almost always cause problems. As a result interpolation on a log scale is used to fill in PSD with lots of points.

If a PSD's frequency vector is defined by the vector x and the PSD's magnitude by y then interpolating a new vector of frequencies xi can be done using the interp1q command as follows

 >> logX = log10(x);
 >> logY = log10(y);
 >> logXi = log10(xi);
 >> yi = 10.^interp1q(logX, logY, logXi);


  • yi is the interpolated PSD magnitudes corresponding to the frequencies of xi.