The article discusses a method for optimal signal and image processing based on subband representations, which involves partitioning a certain frequency range into adjacent subbands. It is shown that many significant signal processing tasks, particularly digital filtering, can be efficiently addressed using subband representations. For solving signal processing problems, it is proposed to employ a mathematical framework based on orthonormal bases of eigenvectors of subband matrices. A mathematical apparatus is presented that allows calculating the portion of signal or image energy corresponding to a given subband without the need for direct computation of Fourier transforms. Criteria for optimal bandpass filtering of one-dimensional signals and two-dimensional images have been developed, enabling effective extraction of useful information and suppression of noise. The method is illustrated by numerical experiments demonstrating the advantages of the subband approach in digital filtering and data approximation.