How can I calculate the frequency using different color bands?
From a practical perspective, there's good news and there's bad news.  The good news is that, in a sense, consumer grade digital cameras [at least] already do something like what you're describing, so there's a large amount of information available about the process, which is called demosaicing.  The bad news is that, in "standard" designs, the various RAW color channels actually have lower resolution than the physical sensor array, and the color channels in non-RAW images have already been reconstructed. 

The reason for this is that the physical sensors only detect light intensity (not color), and therefore each available physical "pixel" is paired with a color filter, according to some pattern. For example, the Bayer Filter is a common pattern which allocates 50% of the available spatial resolution to the green channel, but only 25% each to the red and blue channels.  The various spatial patterns are called Color Filter Arrays (CFAs).  In effect they model the idea of separate RGB sensors, just in a more cost-effective manner.  If there is some way of exploiting "spectral crosstalk" from the materials used in a given CFA, it would be handled in the context of demosaicing. 

That means, if you're dealing with a camera which uses that type of sensing scheme, the most reasonable thing you can hope for is access to the camera RAW data (i.e. un-demosaiced), from which you can apply a higher-quality demosaicing algorithm to reconstruct the image.  From the wiki:


  When one has access to the raw image data from a digital camera, one
  can use computer software with a variety of different demosaicing
  algorithms instead of being limited to the one built into the
  camera...The differences in rendering the finest detail (and grain
  texture) that come from the choice of demosaicing algorithm are among
  the main differences between various raw developers; often
  photographers will prefer a particular program for aesthetic reasons
  related to this effect.


The following link seems to be a good overview of various reconstruction algorithms:

A Study of Spatial Color Interpolation Algorithms for Single-Detector Digital Cameras

In higher-end cameras, however, the RAW color channels might not even be spatially interleaved.  Two of the different higher-end schemes (beam splitting, temporal interleaving) are reviewed here.

One type of sensor that I think works more like what you had in mind is the Foveon X3 Sensor. The following paragraph from the link gives a good overview of the resolution issues:


  For example, the dimensions of the photosite array in the sensor in
  the Sigma SD10 camera are 2268 × 1512, and the camera produces a
  native file size of those dimensions (times three color layers). This
  amounts to approximately 3.4 million three-color pixels. However, it
  has been advertised as a 10.2 MP camera by taking account of the fact
  that each photosite contains stacked red, green, and blue color
  sensing photodiodes, or pixel sensors (2268 × 1512 × 3). By
  comparison, the dimensions of the photosite array in the 10.2 MP Bayer
  sensor in the Nikon D200 camera are 3872 × 2592, but there is only one
  photodiode, or one pixel sensor, at each site. The cameras have equal
  numbers of photodiodes, and produce similar RAW data file sizes, but
  the Bayer filter camera produces a larger native file size via
  demosaicing.


I think this is what you're looking for, assuming I understood the question.