Echo Cancellation - A Likelihood Ratio Test for Double-talk Versus Channel Change

Echo cancellers are in wide use in both electrical (four wire to two wire mismatch) and acoustic (speaker-microphone coupling) applications. One of the main design problems is the control logic for adaptation. Basically, the algorithm weights should be frozen in the presence of double-talk and adapt quickly in the absence of double-talk. The control logic can be quite complicated since it is often not easy to discriminate between the echo signal and the near-end speaker. This paper derives a log likelihood ratio test (LRT) for deciding between double-talk (freeze weights) and a channel change (adapt quickly) using a stationary Gaussian stochastic input signal model. The probability density function of a sufficient statistic under each hypothesis is obtained and the performance of the test is evaluated as a function of the system parameters. The receiver operating characteristics (ROCs) indicate that it is difficult to correctly decide between double-talk and a channel change based upon a single look. However, post-detection integration of approximately one hundred sufficient statistic samples yields a detection probability close to unity (0.99) with a small false alarm probability (0.01)

Structured Compressed Sensing: From Theory to Applications

Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using matrices of randomized nature and signal models based on standard sparsity. In recent years, CS has worked its way into several new application areas. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured sensing architectures that correspond to the characteristics of feasible acquisition hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode broader data models, including continuous-time signals. In our overview, the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware. Our summary highlights new directions as well as relations to more traditional CS, with the hope of serving both as a review to practitioners wanting to join this emerging field, and as a reference for researchers that attempts to put some of the existing ideas in perspective of practical applications.Comment: To appear as an overview paper in IEEE Transactions on Signal Processin