An orthogonal set of frequency and amplitude modulated (FAM) functions for variable resolution signal analysis

A general formula for defining a wide class of orthogonal functions is given. The class is based on circular sine and cosine functions which are simultaneously frequency and amplitude modulated in such a way that they remain orthogonal. This is achieved with any choice of FM or AM function. The class, which is called FAM functions, offers a practical and flexible tool for signal processing. They have been used to produce nonuniform resolution auditory spectrograms. The achieved time-frequency resolution is of very high quality. The preliminary results show that they are approaching the theoretical limit given for the Δf-Δt product. The orthogonality of the FAM functions is proved, how a complex orthogonal auditory transform (OAT) can be realized by FAMs is described, and a method for constructing a complex orthogonal one Bark filter bank for signal analysis and psychoacoustic experimentation is given