This paper presented a complex valued transform for speech analysis based on modulation frequencies. Low modulation frequencies contain crucial cues for speech intelligibility so the idea was to exploit that property in combination to the great sparsity of the non redundant complex wavelet transform. It can primarily be used for speech denoising in a modulation subband approach but also shows interesting capabilities for compression. The CxWT offers useful phase information to the Complex Modulation "Spectrum" that allows joint work on both magnitude and phase. Precisely what was needed to do filtering in the modulation domain.
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