A novel description and mathematical analysis of the Fractional Discrete Fourier Transform

I discuss the nature of a Fractional Discrete Fourier Transform (FrDFT) described algorithmically by a combination of chirp transforms and ordinary DFTs. The transform is shown to be consistent with a continuous two-dimensional rotation between the time and frequency domains. I further present a new closed-form expression for the transformation matrix and some preliminary analysis of its properties.