From gudehus@128.140.57.84 Mon Sep 18 10:17:02 1995 Path: solitaire.cv.nrao.edu!hearst.acc.Virginia.EDU!maui.cc.odu.edu!news.larc.nasa.gov!news.msfc.nasa.gov!pecos.msfc.nasa.gov!not-for-mail From: gudehus@128.140.57.84 (Donald H. Gudehus) Newsgroups: sci.astro.research Subject: Re: Aliasing and dithering Date: 12 Sep 1995 17:07:40 -0500 Organization: Emory University Lines: 36 Sender: astres@pecos.msfc.nasa.gov Approved: astres@pecos.msfc.nasa.gov Distribution: world Message-ID: <4350bc$21m@pecos.msfc.nasa.gov> Reply-To: gudehus@128.140.57.84 NNTP-Posting-Host: pecos.msfc.nasa.gov Keywords: techniques Peter Newman writes: >1) How do you avoid aliasing problems when re-binning digital spectra >(e.g. using the _scrunch_ command in Figaro)? I suspect I need to worry >about mutual primeness of the bin sizes before and after, but since the >original data is not linearly binned, I am a bit stuck. References or >methods appreciated. While I am not familiar with Figaro, scrunching (on evenly sampled data, but not necessarily evenly spaced in some physical variable) involves establishing the mathematical relationship between the old and new physical spatial variables, inverting the relationship to pick out the old variable values corresponding to the desired spacing of the new variable, and then using a good interpolation method (usually a tapered sinc) to obtain the intensity at the old interpolated positions. The intensities, which can be flux preserved if desired by multiplying by the derivative, are written to the evenly spaced locations in the new physical variable. For example, if a spectrum recorded on a CCD has a nonlinear relationship between wavelength and pixel location, one establishes a calibration that describes that situation and then rebins to create a linear relationship. One can go further, by purposely creating a nonlinear (but controlled) relationship, say log(wavelength) for the new rebinned data. The sinc interpolation is optimal for interpolation on even sampled data, however one normally has to taper the contributions of the higher order terms. Aliasing should not be a problem unless you wind up being undersampled in the new rebinned relation. If this is the case, an intermediate highly sampled version can be filtered and then rebinned to a lower sample rate. For some code on this topic see DUA4:[MIIPS.FOR]SCRUNCH.FOR and the called subroutines at vms.ucc.okstate.edu, accessible via anonymous ftp. Donald Gudehus dgudehu@emrycc.cc.emory.edu From ajc@reaxp01.roe.ac.uk Tue Sep 19 18:05:33 1995 Path: solitaire.cv.nrao.edu!hearst.acc.Virginia.EDU!caen!news.umass.edu!umassd.edu!ulowell.uml.edu!news.cs.umb.edu!oitnews.harvard.edu!yale!gumby!newsxfer.itd.umich.edu!newsfeed.internetmci.com!news.msfc.nasa.gov!pecos.msfc.nasa.gov!not-for-mail From: ajc@reaxp01.roe.ac.uk (Andrew Cooke) Newsgroups: sci.astro.research Subject: Re: Aliasing and dithering Date: 18 Sep 1995 10:32:51 -0500 Organization: Institute for Astronomy, Royal Observatory Edinburgh Lines: 34 Sender: astres@pecos.msfc.nasa.gov Approved: astres@pecos.msfc.nasa.gov Distribution: world Message-ID: <43k3f3$4k1@pecos.msfc.nasa.gov> Reply-To: A.Cooke@roe.ac.uk NNTP-Posting-Host: pecos.msfc.nasa.gov Keywords: techniques i asked about interpolation (especially wrt spectra) on this group last year. i posted a summary which, hopefully, is archived somewhere - check the FAQ? basically, sinc interpolation is the `best' you can do to estimate the spectrum at positions other than the centre of the bins in the original spectra, but it does horrible things to any simple error analysis you might hope to use later. for good quality data, sinc interpolation is probably the way to go. for noisy data it's not so nice - you can get -ve values if you're really unlucky. iraf has sinc interpolation in one dimension, but i don't think figaro does. andrew (p.s. there does not seem to be a FAQ for this group on the www at http://www.cis.ohio-state.edu/hypertext/faq/usenet ) In article <4350bc$21m@pecos.msfc.nasa.gov>, Donald H. Gudehus wrote: >Peter Newman writes: > >>1) How do you avoid aliasing problems when re-binning digital spectra >>(e.g. using the _scrunch_ command in Figaro)? I suspect I need to worry >>about mutual primeness of the bin sizes before and after, but since the >>original data is not linearly binned, I am a bit stuck. References or >>methods appreciated. -- A.Cooke@roe.ac.uk work phone 0131 668 8357 home phone/fax 0131 667 0208 institute for astronomy, royal observatory, blackford hill, edinburgh http://www.roe.ac.uk/ajcwww