Bomem-GRAMS User's Guide
Bomem-GRAMS User's Guide
Bomem-GRAMS User's Guide
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Appendix A<br />
Apodization Functions<br />
Name and description Function FWH<br />
H (%)<br />
Cosine<br />
Small side lobes, although with appreciable<br />
ripple; intermediate half-width.<br />
Hamming (Happ-Genzel)<br />
Small side lobes, although with appreciable<br />
ripple; intermediate half-width.<br />
Blackman-Harris<br />
Extremely small side lobes; large half width.<br />
Gaussian<br />
Monotone decreasing function with no ripple<br />
(minor ripple due to finite length).<br />
( cosπD)<br />
SLAM<br />
(%)<br />
0 .5 + 0.5<br />
91 0.71<br />
( cosπD)<br />
0 .53856 + 0.46144<br />
91 0.71<br />
0 .42323 + 0.49755( cosπD)+<br />
0.07922(cos 2π D)<br />
116 0.04<br />
e<br />
2<br />
-3.91202300543D<br />
75 0.1<br />
Norton Beer weak* 2<br />
0.548<br />
− 0.08331 ( − D )+ 0.5353(1<br />
− D<br />
2 ) 2 72 5.8<br />
Norton Beer medium* 2<br />
0.261−<br />
0.1548381 ( − D )+ 0.894838(1<br />
− D<br />
2 ) 2 84 1.4<br />
Norton Beer strong* 2 2<br />
0.09 + 0.5875( 1−<br />
D ) +<br />
0.3225(1<br />
− D<br />
2 ) 4<br />
97 0.3<br />
* Functions taken from the article New Apodization Functions for Fourier Spectrometry by Robert H. Norton and<br />
Reinhard Beer, J. Opt. Soc. Am., Vol. 66, No. 3, March 1976, pp. 259-264.<br />
These functions are an attempt to provide optimum apodizing functions of algebraic form that provide the smallest<br />
degradation in resolution for a specified reduction in side lobe intensity.<br />
Although these three functions provide optimum performance in terms of FWHH/SLAM ratio, they have the drawback of<br />
exhibiting very slow damping of the side lobe features (large ripple), which is often undesirable.<br />
32 <strong>Bomem</strong>-<strong>GRAMS</strong> <strong>User's</strong> <strong>Guide</strong>
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