Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> Cepstral Filtering <s> An approach to some nonlinear filtering problems through a generalized notion of superposition has proven useful In this paper this approach is investigated for the nonlinear filtering of signals which can be expressed as products or as convolutions of components. The applications of this approach in audio dynamic range compression and expansion, image enhancement with applications to bandwidth reduction, echo removal, and speech waveform processing are presented. <s> BIB001 </s> Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> Cepstral Filtering <s> The minimum-phase components of source waveforms can be recovered by blind dereverberation using the minimum-phase complex cepstrum. This recovery process is robust for changes in the transfer functions (TFs), since the all-pass components of the responses that are highly sensitive to changes in the TFs can be disregarded. Yet it is still necessary to keep all-pass information if the timing of the source event is required. Dereverberation of reverberant speech signals requires the all-pass components to keep the pitch information. > <s> BIB002
Oppenhiem et al. BIB001 proposed a single microphone dereverberation approach, using the cepstral filtering technique in which speech is considered as slowly varying in the cepstral domain, with its cepstral components concentrated around the cepstral origin. Whereas, the acoustic impulse response is characterized by the pulses with rapid ripples concentrated far away from the cepstral origin BIB001 . The complex cepstrum of reverberant speech z(n) can be represented as where C h (n) is the complex cepstrum of the reverberant impulse response and C s (n) is the complex cepstrum of the speech signal. Therefore, the dereverberation can be achieved by removing the cepstral components corresponding to the impulse response by applying low time lifter in cepstral domain. Also discussed in BIB001 was an alternative approach, where a cepstral filtering procedure using a comb filter is considered for reducing the reverberation effect. The cepstral filtering has been successfully applied to the enhancement of speech degraded by simple echoes BIB001 . Typically, frame based processing is used to calculate the cepstrum of a signal. Since reverberation effects are generally much longer than typical frame lengths, the current frame does not contain all the reverberation effects of the frame, while it also contains reverberation effects from previous frames. Besides, the cepstrum of the clean speech signal C s (n) and the cepstrum of the acoustic impulse response C h (n) typically have a large overlap, resulting in signal distortion when using low time filtering. By using an exponential windowing procedure and cepstral averaging in order to identify the room impulse response h(n) before inverse filtering, a significant improvement is possible BIB002 . However, in practice, single-microphone cepstrum based techniques for dereverberation have a limited performance.