Effects of dispersion resampling (interpolation) on the SNR
Frank Valdes wrote on Dec 15, 1997
I have studied the noise behavior of spectral interpolation with a precisely quantifiable test. I created a 1D spectrum with a signal of exactly 1000 and a Gaussian noise with sigma of 25 (SNR=40). I then shifted this spectrum by 0.1 pixels to 0.5 pixels using DISPCOR with "poly5" interpolation. I also shifted the original by 0.5 pixels using "linear" interpolation and "sinc" interpolation. The standard deviation is show below as measured by IMSTAT. This shows the magnitude of the interpolation smoothing on the noise. Note that in a real dispersion correction the pixel shifts relative to the input spectrum will vary in some uniform way between no shift and the maximum of a shift exactly between two input pixels. # IMAGE NPIX MEAN STDDEV MIN MAX original spec.imh 501 999.3 25.19 931.8 1089. poly5 +.1 pixel spec3.imh 500 999.3 21.07 941.1 1066. poly5 +.2 pixel spec4.imh 500 999.3 20.76 942.0 1061. poly5 +.3 pixel spec5.imh 500 999.2 20.36 941.7 1057. poly5 +.4 pixel spec6.imh 500 999.2 20.00 941.6 1057. poly5 +.5 pixel spec1.imh 500 999.2 19.84 943.8 1062. linear +.5 pixel spec2.imh 500 999.2 17.72 954.7 1055. sinc +.5 pixel spec7.imh 500 999.2 25.03 915. 1074. So with "poly5" interpolation you can expect an apparent reduction in the SNR of up to 22% due to smoothing of the data by the dispersion correction resampling. This can be avoided by using "linearize=no" in DISPCOR and the other spectral reduction tasks that call DISPCOR. Sinc interpolation offers interpolation that minimizes noise smoothing but has the hazard that around cosmic rays or marginally sampled sharp features ringing of the interpolator will extend a long way from the feature. Frank Valdes
Last post on Dec 15, 1997