Audio bandwidth extension based on temporal smoothing cepstral coefficients

Xin Liu,Chang-Chun Bao

doi:10.1186/s13636-014-0041-6

Abstract

In this paper, we propose a wideband (WB) to super-wideband audio bandwidth extension (BWE) method based on temporal smoothing cepstral coefficients (TSCC). A temporal relationship of audio signals is included into feature extraction in the bandwidth extension frontend to make the temporal evolution of the extended spectra smoother. In the bandwidth extension scheme, a Gammatone auditory filter bank is used to decompose the audio signal, and the energy of each frequency band is long-term smoothed using minima controlled recursive averaging (MCRA) in order to suppress transient components. The resulting ‘steady-state’ spectrum is processed by frequency weighting, and the temporal smoothing cepstral coefficients are obtained by means of the power-law loudness function and cepstral normalization. The extracted temporal smoothing cepstral coefficients are fed into a Gaussian mixture model (GMM)-based Bayesian estimator to estimate the high-frequency (HF) spectral envelope, while the fine structure is restored by spectral translation. Evaluation results show that the temporal smoothing cepstral coefficients exploit the temporal relationship of audio signals and provide higher mutual information between the low- and high-frequency parameters, without increasing the dimension of input vectors in the frontend of bandwidth extension systems. In addition, the proposed bandwidth extension method is applied into the G.729.1 wideband codec and outperforms the Mel frequency cepstral coefficient (MFCC)-based method in terms of log spectral distortion (LSD), cosh measure, and differential log spectral distortion. Further, the proposed method improves the smoothness of the reconstructed spectrum over time and also gains a good performance in the subjective listening tests.

Highlights

In current mobile communication systems, the effective bandwidth of the transmitted wideband (WB) audio is limited to the frequency range of 50 ~ 7,000 Hz
The joint probability density function of the HF and LF feature vectors is approximated by a Gaussian mixture model (GMM), and the HF spectral envelope is estimated according to the minimum mean square error (MMSE) criterion [11,12]
5 Conclusions This paper presents a novel bandwidth extension (BWE) method based on temporal smoothing cepstral coefficients (TSCC)

Summary

Introduction

In current mobile communication systems, the effective bandwidth of the transmitted wideband (WB) audio is limited to the frequency range of 50 ~ 7,000 Hz. 2.1.1 Minima controlled recursive averaging In the proposed method, MCRA [28] is first employed to extract the ‘steady-state’ components from the audio energy spectrum, and the adverse effects of BWE caused by the transient components are restrained in the frontend. In order to make a balance between temporal smoothness of the extended spectrum and mutual dependencies between the LF and HF parameters, the resulting ‘steady-state’ spectrum is further used to remove the transients from the original spectrum Sf(m,j) of audio signals by the spectral weighting method. Compared with the ‘steady-state’ spectrum shown, spectral weighting does repress the transient components and preserves more fine structure which is beneficial to describe the time-frequency characteristics of audio signals. Discrete cosine transform (DCT) is applied to de-correlate the coefficients, and the resulting cepstral coefficients are referred to as TSCCs, Cðm; rNffi2ffiffiffiX1i1⁄490Scðm; iÞ jπ cos 2N ð2i þ

HF spectral envelope estimator based on Gaussian mixture model

Cosh measure

Conclusions