Reality preserving fractional transforms [signal processing applications]

The unitarity property of transforms is useful in many applications (source compression, transmission, watermarking, to name a few). In many cases, when a transform is applied on real-valued data, it is very useful to obtain real-valued coefficients (i.e. a reality-preserving transform). In most applications, the decorrelation property of the transform is of importance and it would be very useful to control it under some transform parameter (e.g. in joint source-channel coding). This paper focuses on fractional transforms, as tools for obtaining such properties. We propose a methodology for obtaining them and obtain variants of the discrete fractional cosine (sine) transform which share real-valuedness as well as most of the properties required for a fractional transform matrix. As shown in (I. Venturini et al. IEEE Trans. Signal Proc.), such matrices cannot be symmetric.