Artificial bandwidth extension of a speech signal is a way to improve speech quality and intelligibility in narrowband telephonic communication. Artificial bandwidth extension techniques extend the bandwidth of narrowband signals using only narrowband information available at the receiver end. This work proposes a new bandwidth extension technique based on the $H^{\infty }$ sampled-data control theory and deep neural network (DNN) regression approach for recovering the missing high-frequency components of the speech signal. The $H^{\infty }$ sampled-data control theory helps in designing of a synthesis filter by optimally utilizing the inter-sample information of a signal and a signal model. The obtained synthesis filter is further used to recover the high-frequency information of the signal. The non-stationary (time-varying) characteristic of speech signals mandates numerous synthesis filters for reconstructing the whole speech signal. Hence, a DNN model is used for estimating the synthesis filter information and a gain factor for specified narrowband information of an unseen signal. Objective analysis is done on the TIMIT and RSR15 datasets. Subjective analysis is done on the RSR15 dataset.

语音信号的人工带宽扩展是提高窄带电话通信中语音质量和可懂度的一种方式。人工带宽扩展技术仅使用接收端可用的窄带信息来扩展窄带信号的带宽。这项工作提出了一种新的带宽扩展技术，基于$H^{\infty }$采样数据控制理论和深度神经网络 (DNN) 回归方法，用于恢复语音信号丢失的高频分量。这$H^{\infty }$采样数据控制理论通过优化利用信号的样本间信息和信号模型来帮助设计合成滤波器。得到的合成滤波器进一步用于恢复信号的高频信息。语音信号的非平稳（时变）特性需要大量合成滤波器来重建整个语音信号。因此，DNN 模型用于估计未见信号的指定窄带信息的合成滤波器信息和增益因子。客观分析是在 TIMIT 和 RSR15 数据集上完成的。主观分析是在 RSR15 数据集上完成的。