Index of content:
Volume 125, Issue 1, January 2009
- ACOUSTIC SIGNAL PROCESSING 
125(2009); http://dx.doi.org/10.1121/1.3006385View Description Hide Description
When one visualizes a sound field as a means of treating noise sources, a detailed variation of the sound field is not required. It is sufficient to see source locations and overall variation of the field. A complex envelope in space can provide adequate information that one wishes to get because an envelope shows a gross change in signal. In other words, to interpret overall variation of sound fields in terms of a complex envelope is attempted. To achieve this objective, spatial complex envelopes have been defined firstly, and then a spatial modulation method to obtain the envelope has been theoretically developed and verified.
125(2009); http://dx.doi.org/10.1121/1.3021435View Description Hide Description
During November 1994, broadband acoustic signals were transmitted from a source to a 20-element, vertical array at approximately range in the eastern North Pacific Ocean as part of the acoustic engineering test (AET) of the acoustic thermometry of ocean climate program [Worcester et al., J. Acoust. Soc. Am.105, 3185–3201 (1999)]. The AET tomography signal can be treated as a binary-phase shift-keying communication signal with an information rate of . With the multipath arrivals spanning , these data represent an extreme case of intersymbol interference. The AET array data are processed using time reversal combined with frequent channel updates to accommodate channel variations over the long reception, followed by a single channel decision-feedback equalizer. The almost error-free performance using all 20 array elements demonstrates the feasibility of time reversal communications at basin scale. Further, comparable performance of single receive element communications integrating over multiple transmissions indicates that the ocean provided temporal diversity that is as effective as the spatial diversity provided by the array.
The prolate spheroidal wave functions as invariants of the time reversal operator for an extended scatterer in the Fraunhofer approximation125(2009); http://dx.doi.org/10.1121/1.3023060View Description Hide Description
The decomposition of the time reversal operator, known by the French acronym DORT, is widely used to detect, locate, and focus on scatterers in various domains such as underwater acoustics, medical ultrasound, and nondestructive evaluation. In the case of point-scatterers, the theory is well understood: The number of nonzero eigenvalues is equal to the number of scatterers, and the eigenvectors correspond to the scatterersGreen’s function. In the case of extended objects, however, the formalism is not as simple. It is shown here that, in the Fraunhofer approximation, analytical solutions can be found and that the solutions are functions called prolate spheroidal wave-functions. These functions have been studied in information theory as a basis of band-limited and time-limited signals. They also arise in optics. The theoretical solutions are compared to simulation results. Most importantly, the intuition that for an extended objects, the number of nonzero eigenvalues is proportional to the number of resolution cell in the object is justified. The case of three-dimensional objects imaged by a two-dimensional array is also dealt with. Comparison with previous solutions is made, and an application to super-resolution of scatterers is presented.
125(2009); http://dx.doi.org/10.1121/1.3035835View Description Hide Description
A direct imaging algorithm for point and extended targets is presented. The algorithm is based on a physical factorization of the response matrix of a transducer array. The factorization is used to transform a passive target problem to an active source problem and to extract principal components (tones) in a phase consistent way. The multitone imaging function can superpose multiple tones (spatial diversity/aperture of the array) and frequencies (bandwidth of the probing signal) based on phase coherence. The method is a direct imaging algorithm that is simple and efficient since no forward solver or iteration is needed. Robustness of the algorithm with respect to noise is demonstrated via numerical examples.