Aspects of the present disclosure include cancellation systems, methods, apparatuses, and software for acoustic or electromagnetic measurement or communications. In some embodiments, full-duplex measurement and/or communications systems can be implemented that permit simultaneous transmission and reception of signals. A cancellation signal generated in accordance with teachings herein may be produced by iteratively solving a Wiener filter problem and provided to a cancellation transducer to cancel unwanted signals in an analog fashion and/or adaptive cancellation module to cancel unwanted signals in a digital fashion. A number of new techniques for reducing or eliminating unwanted signals are described herein that can be used alone or in combination in order to tailor a signal cancelling system, method, apparatus, or software product to particular uses and environments.