Spectral Distribution
- The basis functions at one location will be distributed
uniformly between 0 and
.
- We will consider the critically complete case where, M = N. Recall
that M is the total number of basis functions and N is the total number
of data points in the original signal.
- We will denote by m1 the number of basis functions at each
location. In the spatial domain the basis functions are placed every D pixels.
Clearly, with this sub-sampling of the N point signal by D, we will
require m1 = D = 8 basis functions at each location in order for
the basis to be complete.
- As mentioned previously, all basis functions in this implementation have
= 3 pixels.
- The following expression, with m counting 0 to 7, finds the 8 uniformily
distributed and centered frequencies between 0 and
and the expression for n from the previous page is used to find the derivative
orders necessary to place spectral peaks at these frequencies.
n = {0, 3, 8, 17, 28, 41, 58, 77}
