e75c4b6c   
   From: DGoncz@replikon.net   
      
   Let us say we want the gradient of a Time series. For finite time series we   
   will be losing one data point at each end using most most methods. We   
   subtract each data point from its adjacent data point the one to either so   
   I'd let's say it's going to be the right side consistency consistently.   
   This gives us the time series which is the gradient of that original signal.   
      
   Let us say we want the gradient of a two-dimensional spatial series   
   otherwise known as an image. Buying analogous process I'm subtracting and   
   getting something like the gradient.   
      
   Symbolically the gradient is the partial derivative in each direction for   
   any number of dimensions.   
      
   Well I have been playing with the two dimensional spatial series data or   
   image format in mathcad and found a function called cfft which computes the   
   complex fast fourier transform of data in 2 dimensions. The icfft function   
   reverses that result to restore an image. Lowpass and high-pass filtering   
   are easy but not spectacularly easy in the cfft domain. They are   
   spectacular easy in the one-dimensional case.   
      
   Pixel data in two dimensions in space in grayscale our conventionally a   
   number of bits say 8 bits for 256 levels of Gray. And are analogous in   
   color spaces. Edge detection produces a result similar to an artist's   
   pencil drawing.   
      
   Well I collect pencil drawings and also pencil drawing software.   
      
   And I use mathcad.   
      
   I usually use the variable name capital m for matrix containing two   
   dimensional grayscale image data in mathcad. I compute the gradient several   
   different ways in method.   
      
   I have a new way to compute the gradient in mathcad and symbolically.   
      
   icfft (i * cfft (M))= grad(M).   
      
   Discussion?   
      
   Douglas   
      
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