* how sinc functions sum together to reconstruct bandlimited signals:
http://ccrma.stanford.edu/~jos/resample/Theory_Ideal_Bandlimited_Interpolation.html

* The reconstructed (continuous) signal from Sinc Interpolation passes through
  all the samples - hence it is a consistent model for the measurements.

* deviation from unity between samples can be thought of as ``overshoot'' or 
  ``ringing'' of the lowpass filter which cuts off at half the sampling rate, 
  or it can be considered a ``Gibbs phenomenon'' associated with bandlimiting.

* for undersampled, strong features,
  such as cosmic rays or narrow  emission  or  absorption  lines,  the
  ringing  can be more severe than the polynomial interpolations.

* Use sinc interp. to generate "undistorted" level 1-C frames. 

* Sinc interpolation is most optimal method but it does not 
  accomodate bad pixels easily.

* A signal sampled at or above Nyquist can be totally reconstructed.

* A bandlimited signal can be interpolated exactly using sinc interpolation.

* N.B. The PSF acts as a transfer function or "low-pass" filter of the
  true sky! It degrades high frequency information. The pixels "sample"
  this "continuous" low-pass (or band-limited) transfer function. 

* sinc interpolation is used in image processing when the
  following conditions apply:

    - perfect data (no noise)

    - the original image is bandwidth limited (for an optical
    spectrum this limiting is a result of the instrument response
    function)

    - the sampling is above the nyquist frequency for the
    bandwidth limited original.

    - the sampled signal is, mathematically, the product of
    equally spaced delta functions with the data.

    if these conditions hold then convolution with a sinc function
    gives a perfect re-construction of the data (which can be
    resampled wherever you want).

    this is clear from pratt's `digital image processing', for
    example.


    minor problems occur because:

    - the sampling is not a delta function but something rather
    irregular across a ccd `bin' (this was described in an
    issue of gemini - the newsletter for the la INT telescopes)

    - the instrument reponse function may have some high-frequency
    response.


    major problems occur because:

    - noise spikes, radhits corrupt large regions.

    - the resultant noise is correlated over many bins and very
    difficult to interpret when model fitting.  this is true for
    any interpolation scheme, but there are a few `fudges' that
    can be used if only nearest neighbours are used in interpolation
    (email me if interested).


    other reading includes bracewell's book on fourier transforms,
    brault + white (a&a 13 169 (1971)) and numerical recipes
    (press et al) (various bits, including matched filters).