A new linear time-frequency paradigm

We propose a new linear time-frequency (TF) paradigm, in which the value of a signal at any time is distributed in frequency. Starting with the short time Fourier transform (STFT) representation of a signal, we apply a morphing process, based on the channelized instantaneous frequency (GIF), to obtain a new TF representation. When applied to a multicomponent signal which has linearly independent components and which satisfies a separability condition, the process produces a TF representation in which the value of each signal component is distributed along the component's instantaneous frequency curve in the time-frequency plane. The method is linear on the span of the signal's components, and cross-terms, which make it difficult for conventional TF methods to isolate individual components, do not occur. The individual components are effectively isolated in the new representation, and may be recovered by a straight-forward integration. We apply die new technique to remove an additive sinusoidal FM interferer from a speech signal, and demonstrate its superiority to either the STFT or standard spectral subtraction.