Filter design based on the fractional Fourier transform associated with new convolutions and correlations

We introduce new convolutions and correlations associated with the Fractional Fourier Transform (FrFT) which present a significant simplicity in both the time and FrFT domains. This allows for several consequences and applications, among which we highlight the design of some multiplicative filters in the FrFT domain having a significant simplicity when compared with the already known ones. Thus, this has consequences, e.g., in signal filtering due to the need of modification of a calculated signal to remove undesirable aspects of the signal before it is used in a calculation or a controller. In special, we propose a new filter design implementation which exhibits advantages in comparison to other known ones. Concrete examples are presented to illustrate the theory.