Homomorphic filtering in the spatial domain can avoid the problems described above. The filtering can be performed by precomputing the inverse fourier transform of the filter function:
The filter can then be applied via convolution. From equations 6.5 through 6.7 we get:
This method has a drawback of its own. The convolution performed in Equation 6.9 can be computationally expensive if the convolution mask, , is large. Of course, we could use a smaller mask that approximates as described in .
The following section describes another approximation that yields good results and has a simpler implementation.