Diatoms are unicellular algae that have as characteristic to be composed mainly of silice. Currently, its study has become relevant due to its multiple applications that include forensic medicine, palaeoenvironmental reconstructions and its use as biological bioindicators of water quality. It is estimated that there are around 100,000 different diatom species, showing a high similarity between some of them. For these reasons, their identification is slow and often unreliable. Additionally, the number of specialists capable of carrying out an identification is not sufficient in comparison to the number of samples that usually have to be analyzed. It is for these reasons that there is a need to have automated systems that perform this task. In the present work, an automatic identification system was created for 46 diatom species with different morphology using images obtained with optical microscopy. This system was designed by calculating descriptors in the plane of frequencies using three different methodologies: the Fourier Mellin transform, the concentric ring binary masks and the fractional Fourier transform. The methods used for the identification system has as main characteristics to be robust to changes of scale, rotations, translations, and lighting. Additionally, the number of images used as reference images compared to other techniques found in the literature is lower, which gives a higher possibility that it can be extended to other species.