Methods for extending frequency transforms to resolve features in the spatio-temporal domain

A method implemented in a computer system for processing a digitized electromagnetic signal to identify unwanted signal features comprising

• generating via a particularly configured microprocessor a modified time-frequency representation of an input signal by
• receiving the input signal as a plurality of transform frames in a time domain in the microprocessor, wherein each transform frame includes a plurality of signal samples;
• transforming each transform frame of the input signal into a frequency domain using a frequency transform;
• introducing a time dimension into the frequency transform to generate constant frequency and constant magnitude periodic partial waves for each frequency band of the frequency transform of the input signal for each of the transform frames to form a time-frequency representation for each transform frame;
• applying a smoothing filter to the time-frequency representation to introduce synchronization between the periodic partial waves of adjacent frequency bands and to generate a smoothed time-frequency representation that includes non-periodic wave packets across the frequency bands converted from the periodic partial waves by the synchronization, wherein unwanted signal features are magnified in corresponding frequency bands of the smoothed time-frequency representation for each signal sample in which the unwanted signal features occurred in the input signal in the time domain;
• formulating time-frequency values from the non-periodic wave packets for each frequency band in each signal sample;
• and
• displaying on a display device within the computer system the time-frequency values or representations thereof, or both, identifying the unwanted signal features in discrete time samples.

A non-transitory computer readable storage medium containing instructions for instantiating a special purpose computer to process a digitized electromagnetic signal to remove unwanted signal features from the electromagnetic signal, wherein the instructions implement a computer process comprising the steps of

• receiving the input signal comprising a plurality of transform frames in a time domain;
• transforming the input signal into a frequency domain using a frequency transform;
• generating time-frequency matrices corresponding to respective transform frames from the frequency transform containing basis functions of the frequency transform adjusted for respective transform magnitudes and phases, wherein the time-frequency matrices have a first dimension of time in instances of sample time t and a second dimension of frequency in bandwidth bins k for each transform frame;
• applying a cross-frequency phase coupling processing algorithm between adjacent frequencies to introduce synchronization between the adjacent frequencies and to generate smoothed time-frequency matrices, wherein unwanted signal features are magnified in corresponding bandwidth bins k of the smoothed time-frequency matrices for each time sample tin which the unwanted signal features occurred in the input signal in the time domain;
• and
• outputting for storage or for display on a display device time-frequency values or representations thereof, or both, from the smoothed time-frequency matrices identifying the unwanted signal features for relevant time samples t.