Two-dimensional digital processing of one-dimensional signal

It is of importance to find the necessary and sufficient conditions under which the one-dimensional and two-dimensional processing of any general transform should be equivalent. These conditions are found. It is known that the Fourier transform does not possess the described property. It is shown in this paper that a one-dimensional Fourier transform cannot be equivalent to any two-dimensional transform. On the other hand it is shown that the two-dimensional Fourier transform is equivalent to a one-dimensional transform of another kind and that the processing can be performed by a fast algorithm.