  Artificial bandwidth extension is applied to speech signals to improve their
quality in narrowband telephonic communication. For accomplishing this, the
missing high-frequency (high-band) components of speech signals are recovered
by utilizing a new extrapolation process based on sampled-data control theory
and deep neural network (DNN). The $H^\infty$ sampled-data control theory helps
in designing of a high-band filter to recover the high-frequency signals by
optimally utilizing the inter-sample signals. Non-stationary (time-varying)
characteristics of speech signals forces to use numerous high-band filters.
Hence, we use a deep neural network for estimating the high-band filter
information and a gain factor for a specified narrowband information of the
unseen signal. The objective analysis is done on the TIMIT dataset and RSR15
dataset. Additionally, the objective analysis is performed separately for the
voiced speech as well as for the unvoiced speech as generally needed in speech
processing. Subjective analysis is done on the RSR15 dataset.
