Two-dimensional discrete Hilbert transform and computational complexity aspects in its implementation

It is first shown that the impulse response operator for a two-dimensional discrete Hilbert transform (DHT), although not by itself sum-separable, becomes so after appropriate classification. Subsequently, it is proved that the multiplicative complexity of computation of a two-dimensional DHT is not greater than twice the sum of multiplicative complexities of two one-dimensional DHT´s. Finally, the consequences of Winograd´s algebraical computational complexity theory on the problem considered here are discussed.