Selective Temporal Cepstrum Smoothing for Speech Enhancement

Many speech enhancement algorithms that modify short-term spectral magnitudes of the noisy signal are plagued by annoying spectral outliers that are perceived as musical noise. Especially in nonstationary noise, such as babble-noise or street noise, musical noise artifacts have been an unsolved problem over the last decades. To reduce spectral outliers certain parameters of the speech enhancement algorithm, such as the a priori SNR or the gain function, should be smoothed. However, while a temporal smoothing in the frequency domain reduces spectral outliers, it also results in a distortion of speech onsets and low energy speech components. A better performance can be achieved by applying temporal smoothing in the cepstral domain. The cepstral domain is defined as the inverse Fourier transform of the logarithm of the spectral magnitude. In the cepstral domain, the signal is decomposed into the spectral envelope (lower cepstral coefficients) and the spectral fine structure (upper cepstral coefficients). Speech will be mainly represented by the low cepstral coefficients and a cepstral peak in the upper cepstrum that represents the pitch information. A selective temporal smoothing in this domain can be applied, i.e. no or little smoothing to the speech related cepstral coefficients, and strong smoothing to the remaining coefficients.

The benefits of a selective cepstrum smoothing are that

  • speech onsets are preserved
  • the speech spectral envelopes of plosives and fricatives are preserved
  • spectral harmonics of low energy are preserved
  • the musical noise phenomenon is greatly reduced

Even in babble-noise a selective cepstrum smoothing strongly reduces the musical noise phenomenon without distorting the speech signal. Listening experiments and instrumental measures consistently indicate improvements in terms of overall quality, speech quality, noise quality, noise reduction, spectral distortion and signal-to-noise ratio.

A selective cepstrum smoothing can be applied to any speech enhancement algorithm in that the input spectrum is weighted by a gain function. In speech separation often binary spectral masks are applied. A selective temporal smoothing of the spectral masks in the cepstral domain was shown to greatly improve the overall and background quality of speech separation algorithms.


Colin Breithaupt, Timo Gerkmann, and Rainer Martin, "Cepstral Smoothing of Spectral Filter Gains for Speech Enhancement Without Musical Noise," IEEE Signal Processing Letters, Vol. 14, Issue 12, pp. 1036-1039, Dec. 2007.

Colin Breithaupt, Timo Gerkmann, and Rainer Martin, "A Novel A Priori SNR Estimation Approach Based on Selective Cepstro-Temporal Smoothing," IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), pp. 4897-4900, Apr. 2008.

Nilesh Madhu, Colin Breithaupt, and Rainer Martin, "Temporal smoothing of spectral masks in the cepstral domain for speech separation," IEEE ICASSP, pp. 45-48, Apr. 2008.