Sub-Nyquist Nonuniform Sampling and Perfect Reconstruction of Speech Signals

The discrete-time speech signals obtained by Nyquist uniform sampling (NUS) have two kinds of redundant samples. One originates from the time-varying instantaneous bandwidth. The other originates from non-compactness of spectral support (SS) in time-frequency domain (TFD). In this paper, the sub- Nyquist nonuniform sampling (SNNS) and the perfect reconstruction (PR) formula are proposed for removing the redundant samples due to the time-varying instantaneous bandwidth (IB) in speech signals. In the proposed method, the instantaneous sampling frequency (ISF) varies, depending on the least upper boundary of spectral support of a speech signal in TFD. The definition of the IB, which determines the ISF and is used for generating the set of samples that represent continuous- time signals perfectly, is given.