LAUSR

We propose a scheme for analog-to-digital (A/D) conversion of a signal that is bandlimited most of the time but contains harmonics of a high frequency occasionally. To enable the capture of the high frequency components, such signals are usually oversampled. This framework is of practical interest in the case of electrical signals wherein one encounters high frequency faults or anomalies from time to time, all of which need to be retained for diagnostic purposes. Existing schemes that rely on oversampling for dithered A/D conversion of bandlimited signals are designed for the worst case and do not take into account the fact that the high frequency anomalies occur rarely. We propose an adaptive A/D conversion scheme that identifies the presence or absence of a high frequency component in a given block of samples by formulating it as a hypothesis testing problem. The proposed scheme performs better in terms of compression compared to a scheme designed for the worst case while retaining the same guarantees on the reconstruction error.