• funconv(M, f)—Convolution of matrix M with frequency domain function f.
• funcdeconv(M, f, e)—Deconvolution of matrix M with frequency domain function f and error e.
• matconv(M, N)—Convolution of matrix M with frequency domain mask N.
• matdeconv(M, N, [e])—Deconvolution of matrix M with frequency domain mask N and error e.
These functions convolve, or deconvolve, an image with a function f, or mask N, by multiplying the two together in spatial frequency (the Fourier transform domain). Filtering in the frequency domain can result in a variety of smoothing, edge detection, and periodic noise-reduction operations, depending upon the chosen function or mask. It is often mathematically more efficient to filter in the transform domain, or easier to define filters, than by using convolution in the image domain.
The functions return a matrix containing the convolved image in the image domain.
PTC Mathcad Fourier transforming algorithms in two dimensions return the zero-frequency component in the upper left-hand corner.
Arguments
• M is an image matrix in the spatial or frequency domain.
• N is matrix of real numbers.
• f is a real-valued function in one variable.
• e (optional for matdeconv) is a positive real number.