Signals generated in circuits that include nano-structured elements typically have strongly distinct characteristics, particularly the hysteretic distortion. This is due to memristance, which is one of the key electronic properties of nanostructured materials. In this article, we consider signals generated from a memrsitive circuit model. We demonstrate numerically that such signals can be efficiently represented in certain custom-designed nonorthogonal bases. The proposed method ensures that the actual numerical representation can be implemented as a fast, O(N logN), algorithm. In addition, we discuss the possibility of modelling the hysteretic distortion via fast numerical transforms.