Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6960141 | Signal Processing | 2014 | 7 Pages |
Abstract
We derive a family of discrete window functions for the N-point Fourier transform for application in spectral analysis that optimize the root mean square (RMS) frequency width ÏÏ for a given temporal RMS width Ït. The window family yields as a byproduct the minimum time-bandwidth product ÏÏÏt for given Ït and N. The new windows interpolate for decreasing Ït between the popular Cosine-window and a nearly Gaussian window. The new “confined Gaussian” window function gk(cG) (with k=0,â¦,Nâ1) is extremely well approximated by gk(acG)âG(k)âG(â1/2)[G(k+N)+G(kâN)]/[G(â1/2+N)+G(â1/2âN)] with the Gaussian G(x)=exp[âδt2(xâ(Nâ1)/2)2/(4s2)], the temporal width sâÏt, and time step δt.
Related Topics
Physical Sciences and Engineering
Computer Science
Signal Processing
Authors
Sebastian Starosielec, Daniel Hägele,