Comparison of fitting in time- and Legendre - domain.

Abstract

<p>(<b>a</b>) LMA fit (dashed, red) and mean (cont.) of a noisy exponential with offset in the time domain. Poisson noise; offset, 100; gaussian offset noise with . (<b>b</b>) Legendre spectrum of the same noisy exponential (gray) and LMA fit in the Legendre space (red). (<b>c,d</b>) Probability density function giving the frequency with which the fitted amplitude, normalized to the true value (<b>c</b>), or with which the fitted time constant, normalized to the true value (<b>d</b>)occurs in 5000 trials. True values assumed in c,d: A = 3000, tau = 0.1. All weights set to 1. The red and gray curves give the frequencies resulting from the fits carried out in the time (gray) or Legendre (red) domain, respectively. (<b>e,f</b>) Probability density functions as in (<b>c,d</b>), except that the data were weighted with . The four calculated pdf's in <b>c</b> through <b>f</b> are fitted by Gaussians.</p

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