John R. Buck

Iterative and sequential algorithms for multisensor signal enhancement

In problems of enhancing a desired signal in the presence of noise, multiple sensor measurements will typically have components from both the signal and the noise sources. When the systems that couple the signal and the noise to the sensors are unknown, the problem becomes one of joint signal estimation and system identification. The authors specifically consider the two-sensor signal enhancement problem in which the desired signal is modeled as a Gaussian autoregressive (AR) process, the noise is modeled as a white Gaussian process, and the coupling systems are modeled as linear time-invariant finite impulse response (FIR) filters. The main approach consists of modeling the observed signals as outputs of a stochastic dynamic linear system, and the authors apply the estimate-maximize (EM) algorithm for jointly estimating the desired signal, the coupling systems, and the unknown signal and noise spectral parameters. The resulting algorithm can be viewed as the time-domain version of the frequency-domain approach of Feder et al. (1989), where instead of the noncausal frequency-domain Wiener filter, the Kalman smoother is used. This approach leads naturally to a sequential/adaptive algorithm by replacing the Kalman smoother with the Kalman filter, and in place of successive iterations on each data block, the algorithm proceeds sequentially through the data with exponential weighting applied to allow adaption to nonstationary changes in the structure of the data. A computationally efficient implementation of the algorithm is developed. An expression for the log-likelihood gradient based on the Kalman smoother/filter output is also developed and used to incorporate efficient gradient-based algorithms in the estimation process. >

Active and cooperative learning in signal processing courses

This work describes positive effects of using active and cooperative learning (ACL) methods to improve signal processing instruction. It provides examples, references, and assessment data that encourage other instructors to consider this approach. Conclusions are based on impressions gathered through conversations with students during office hours as well as on responses from anonymous student opinion surveys. In addition to these subjective assessments, preliminary quantitative data measured with the signals and systems concept inventory (SSCI) support the benefits of ACL techniques in signal processing courses.

The use of Zipf's law in animal communication analysis

I nformation theory has been discussed as a technique to analyse communicative processes or sequential behaviour of nonhuman animals, as in MacKay (1972), Slater (1973) and Bradbury & Vehrencamp (1998, chapters 13–15) among others. Recently, McCowan et al. (1999) proposed the use of information theory for their study of bottlenose dolphin, Tursiops truncatus, whistles. They discussed several aspects of their analysis techniques. Although we agree about the effectiveness of information theory to analyse unknown sources, we would like to further the discussion of one analysis method used in McCowan et al. (1999). Specifically, we wish to illustrate that Zipf’s law is of little use in the analysis of communication signals. The presence or absence in dolphins and other animals of some features of human language remain intriguing and open questions (Tyack 1999). However, we assert that a Zipf-based technique is methodologically inappropriate to address these questions. McCowan et al. (1999, page 410) noted that ‘Few investigators of animal behaviour have examined the use of first-order entropic analysis known as Zipf’s law or statistic’. In fact, Zipf’s law has been discarded as a linguistic tool, strongly criticized by Miller (1957), Miller & Chomsky (1963) and more thoroughly by Rapoport (1982). McCowan et al. (1999, page 411) also cite the application of Zipf’s law to DNA sequences by Mantegna et al. (1994) ‘with varying interpretations and reliability (Flam 1994; Damashek 1995; Bonhoeffer et al. 1996; Israeloff et al. 1996; Voss 1996)’. These references’ interpretations vary from strong criticisms of the use of Zipf’s law in the Mantegna et al. study (Bonhoeffer et al. 1996; Israeloff et al. 1996; Voss 1996) to a short news item about

A unified framework for mode filtering and the maximum a posteriori mode filter

A unified framework is presented for examining the performance of linear mode filtering algorithms. Two common mode filters, samples of the mode shapes and the pseudo-inverse of the mode shapes, are presented in this framework as a tradeoff between sensitivity to other modes and sensitivity to white noise. The maximum a posteriori mode filter is presented as an alternative which gracefully transitions between these extremes, and attains the minimum mean squared error when the modes to be estimated are well modeled as samples of a Gaussian random process. Numerical simulations in both shallow and deep water environments confirm the analytically derived properties of these mode filters.

Extending coprime sensor arrays to achieve the peak side lobe height of a full uniform linear array

A coprime sensor array (CSA) is a non-uniform linear array obtained by interleaving two uniform linear arrays (ULAs) that are undersampled by coprime factors. A CSA provides the resolution of a fully populated ULA of the same aperture using fewer sensors. However, the peak side lobe level in a CSA is higher than the peak side lobe of the equivalent full ULA with the same resolution. Adding more sensors to a CSA can reduce its peak side lobe level. This paper derives analytical expressions for the number of extra sensors to be added to a CSA to guarantee that the CSA peak side lobe height is less than that of the full ULA with the same aperture. The analytical expressions are derived and compared for the uniform, Hann, Hamming, and Dolph-Chebyshev shadings.

Beamforming with extended co-prime sensor arrays

Co-prime sensor arrays (CSAs) interleave two uniform linear subarrays that are undersampled by co-prime factors. The resulting nonuniform array requires far fewer sensors to match the spatial resolution of a fully populated ULA of the same aperture. Choosing the co-prime undersampling factors as close to equal as possible minimizes the number of sensors in the CSA. However, the peak side lobe of the CSA is higher than the peak side lobe of the equivalent full uniform linear array (ULA). Increasing the number of sensors in the CSA subarrays by half while maintaining the interelement spacing gurarantees that the CSA peak side lobe is less than that of the full aperture ULA when both arrays use rectangular windows.

Elastomeric Ionic Hydrogel Sensor for Large Strains

An elastomeric hydrogel membrane made of an epoxy-amine network is demonstrated to be a linear strain sensor for large strains up to 20%. Sodium chloride is added in the gel to maintain conductivity at a relatively dry state. The elastic and electrical response are both shown to be linear. Water loss from the hydrogel due to evaporation from the surface is slow. This results in a trend in the impedance of the sensor which can be easily corrected by simple signal processing. A prototype sleeve that uses these sensors for proprioceptive sensing of joint angle motion on a robotic arm is demonstrated as a potential application.

Information theoretic bounds on source localization performance

This paper examines the underwater acoustic source localization problem as an unorthodox communication problem. This perspective produces novel bounds on the performance of any source localization algorithm. The search space is divided into a grid whose cell size is determined by operational constraints. The message transmitted by the source is the cell it is located within. The receiver uses pressure observations from a sensor array to receive this message with a minimum probability of error. A necessary condition to choose the correct grid cell with arbitrarily small positive probability of error is that the mutual information between the source location and the estimate of it must equal or exceed the entropy of the grid. This mutual information can be bounded from above using the Gaussian channel approximation. The source channel coding theorem then determines the minimum necessary SNR to achieve a desired range resolution, or equivalently the best possible range resolution for a given SNR, assuming arbitrarily small probability of error. The resulting resolution bound is discussed in comparison to the Cramer-Rao Bound. The resolution bound is computed for typical underwater environments, and Monte-Carlo experiments are presented for these same environments.

Comparing student understanding of signals and systems using a concept inventory, a traditional exam and interviews

Concept inventories play a growing role in assessing student understanding in engineering curricula. A common application of concept inventories is a pre/post- test assessment in a course. For this reason, it is important to confirm the validity of any new concept inventory, i.e., to verify that the inventory measures what it is designed to assess. The signals and systems concept inventory (SSCI) is a 25-question multiple-choice exam assessing core concepts in undergraduate signals and systems courses. This paper presents two analyses supporting the validity of the SSCI. The first analysis compares the responses of 40 students to final exam questions with their responses to related SSCI questions. This analysis finds statistically-significant correlations between the SSCI and the final exam for questions on convolution and Fourier transform properties. The second analysis examines the interview responses of 18 students to SSCI questions on frequency-selective filtering and convolution. The interviews suggest students have a strong understanding of high and low frequency, have some understanding of the relationship between time and frequency domains, but struggle to interpret frequency responses. The interviews also suggest that many students retain some conceptual understanding of convolution after their memory of the convolution integral has faded.

Response of gray whales to low‐frequency sounds

One transducer from the U.S. Navy SURTASS‐LFA source was used during January 1998 to expose migrating gray whales off the California coast to low‐frequency sound. These transmissions were 42 s in duration, repeating every 6 min, and 160–330 Hz. The whales were observed from shore stations north and south of the source location. Each pod of whales’ closest point of approach (CPA) to the sound source was estimated from the shore observations. The received level (RL) at the CPA was estimated using measured transmission loss curves and the known source level. The probability of observing whale pods at each RL is computed under both playback and control conditions. The difference between these probabilities as a function of RL provides a measure of avoidance for the animals. Previous work [Malme et al. (1984)] found a 50% change in these probabilities at a RL of 120 dB re:1μPa. For an inshore source location, the current work found 50% avoidance occurred at a RL of 141 dB, with 95% confidence bounds of ±3 dB d...