Summary: The author presents possibility of the commonly known adaptive filters algorithms description adjusted to selected orthogonal discrete transformation. Thus the transformation may be selected to represent given signal in a simpler way. The proposed solution is based on the generalized circular convolution concept, while typically the algorithms make use of the filter impulse response resulting from the Fourier frequency theory. The theory is illustrated with the examples of successful simulations for the Haar, Hadamard, Hartley transformations and DCT-III.