Properties for modulation spectral filtering

A two-dimensional representation, the "modulation spectrum", where the modulation frequency exists jointly with a regular Fourier frequency or other filter channel index, has previously been investigated. Accurate modulation filters offer, for example, new approaches for signal separation and noise reduction. However, a filtering operation on modulation frequency components has yet to be carefully defined. Most previous studies on modulation filtering assumed that the amplitude modulation envelope is real and non-negative, which has recently been shown to be incorrect. Distortions appear when the non-negative envelope assumption fails. Beginning with a more appropriate envelope assumption that allows the envelope to go negative, we propose three properties which modulation filtering systems should satisfy. Any modulation filtering method which satisfies these properties yields distortion-free results. An implementation of modulation filtering, based on a short-time Fourier transform followed by independent coherent demodulation for each frequency channel, is then proposed. Satisfaction of the properties is confirmed and an example result of modulation filtering on a speech signal is illustrated.