			       -*- outline -*-

!!! This is work in progress -- highly beta software !!!

* Introduction

In this directory are functions for playing around with irregular
sampled timeseries and for reconstructing the underlying signal if
possible. Irregular means that the sample points are not
taken at equdistant times (i.e. with a constant spacing).

Irregular sampling raises some problems for the classical digital
signal analysis, because the analogies between the continuous
Fourier theory and corresponding discrete algorithms depend on the
regularity of the sampling. If the effects of irregularity are not
explicitly desired often one wants to reconstruct the full
signal information and get a regular representation of it. Thats the
path back to regular DSP and one can forget about the problems of
irregularity again. 

Mathematicians from the Numerical Harmonic Analysis Group
(NuHAG) in Vienna have worked a lot on this problem. There is an
introduction to the irregular sampling problem at 
http://www.unet.univie.ac.at/~a9301647/fsp/irsatour/irsampl.html

All reconstruction algorithms included (at the moment it is only one) 
are mainly based on the work of NUHAG, especially on the work of Thomas
Strohmer ( http://www.math.ucdavis.edu/~strohmer/ ). 

There are some Matlab-Implementations, which
are described in the paper "On the Reconstruction of Irregularly
Sampled Time Series" from Roberto Vio, Thomas Strohmer and Willem
Wamsteker in "Publications of the Astronomical Society of the Pacific,
Vol. 112, pages 74-90, year 2000", which can be requested from the
authors. 

* Some remarks on variable names

A time series consists of a number of pairs of a sampling point and
its corresponding value. A discrete spectrum analogous has frequency
points and frequency values. So repeatedly occuring names are:

XP  -- vector of sampling points
YP  -- vector or matrix of corresponding sampling values
FXP -- vector of frequency points
FYP -- vector or matrix of corresponding frequency values

Names with 'R' as first character contain the corresponding
reconstructed vectors (e.g.: ryp for reconstructed sampling values)

Because the DSP involved here depends on band-limitidness of the
signal 'FMAX' names the band-limiting frequency.

Sampling and frequency points are often rescaled to allow a uniform
treatment. Names with 'N' as last character refer to those normalized
values. 

* Included functions

** Reconstruction of band-limited signals

*** requiring the knowledge of FMAX

irsa_act      : Reconstruction of a band-limited signal from irregular
	        timeseries (relies on irsa_actcore)
irsa_actcore  : Reconstruction of spectrum of a band-limited signal
	        from irregular timeseries 

*** requiring the knowledge of the signal-to-noise ratio

missing, but next to be included

** For generating irregular sampling schemes

irsa_mdsp     : Generates sampling points with a minimum distance
irsa_jitsp    : Generates jittered sampling points

** For generating real-valued irregular timeseries of band-limited signals

irsa_genreal  : Generates irregular timeseries from given amplitudes
                and phases
irsa_rgenreal : Generates irregular timeseries from random amplitudes
                and phases

** Discrete Fourier Transformation

irsa_dft      : The one-dimensional discrete fourier transform
irsa_idft     : The inverse one-dimensional discrete fourier transform

** Resampling

irsa_resample : A function for resampling a band-limited signal on
                arbitrary sample points.

** Helper functions

irsa_normalize: Normalizes time series to a standard scaling 
irsa_dftfp    : Calculates frequency points for the frequency
	        representation of irregular timeseries from given
		sampling points  
irsa_check    : Checks the consistency of given timeseries and
	        computes simple characteristic values
irsa_isregular: Checks if a timeseries is regularly
	        sampled
irsa_plotdft  : Plots amplitudes and phases of a spectrum
		(This is only needed for the demos and does not really
		belong here)

