Kathleen E. Wage

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.

Modal analysis of broadband acoustic receptions at 3515-km range in the North Pacific using short-time Fourier techniques

In 1995-1996 the Acoustic Thermometry of Ocean Climate (ATOC) experiment provided an opportunity to study long-range broadband transmissions over a series of months using mode-resolving vertical arrays. A 75-Hz source off the California coast transmitted broadband pulses to receiving arrays in the North Pacific, located at ranges of 3515 and 5171 km. This paper develops a short-time Fourier transform (STFT) processor for estimating the signals propagating in the lowest modes of the ocean waveguide and applies it to analyze data from the ATOC experiment. The STFT provides a convenient framework for examining processing issues associated with broadband signals. In particular, this paper discusses the required frequency resolution for mode estimation, analyzes the broadband performance of two standard modal beamforming algorithms, and explores the time/frequency tradeoffs inherent in broadband mode processing. Short-time Fourier analysis of the ATOC receptions at 3515 km reveals a complicated arrival structure in modes 1-10. This structure is characterized by frequency-selective fading and a high degree of temporal variability. At this range the first ten modes have equal average powers, and the magnitude-squared coherence between the modes is effectively zero. The coherence times of the peaks in the STFT mode estimates are on the order of 5.5 min. An analysis of mean arrival times yields modal dispersion curves and indicates that there are statistically significant shifts in travel time over 5 months of ATOC transmissions.

Mode coherence at megameter ranges in the North Pacific Ocean

This article analyzes the coherence of low-mode signals at ranges of 3515 and 5171 km using data from the Acoustic Thermometry of Ocean Climate (ATOC) and Alternate Source Test (AST) experiments. Vertical line arrays at Hawaii and Kiritimati received M-sequences transmitted from two sources: the 75-Hz bottom-mounted ATOC source on Pioneer Seamount and the near-axial dual-frequency (28/84 Hz) AST source deployed nearby. This study demonstrates that the characteristics of the mode signals at 5171-km range are quite similar to those at 3515-km range. At 75 Hz the mode time spreads are on the order of 1.5 s, implying a coherence bandwidth of 0.67 Hz. The time spread of the 28-Hz signals is somewhat lower, but these signals show significantly less frequency-selective fading than the 75-Hz signals, suggesting that at the lower frequency the multipaths are temporally resolvable. Coherence times for mode 1 at 75 Hz are on the order of 8 min for the 3515-km range and 6 min for 5171-km range. At 28 Hz mode 1 is muc...

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.

The North Pacific Acoustic Laboratory deep-water acoustic propagation experiments in the Philippine Sea

A series of experiments conducted in the Philippine Sea during 2009-2011 investigated deep-water acoustic propagation and ambient noise in this oceanographically and geologically complex region: (i) the 2009 North Pacific Acoustic Laboratory (NPAL) Pilot Study/Engineering Test, (ii) the 2010-2011 NPAL Philippine Sea Experiment, and (iii) the Ocean Bottom Seismometer Augmentation of the 2010-2011 NPAL Philippine Sea Experiment. The experimental goals included (a) understanding the impacts of fronts, eddies, and internal tides on acoustic propagation, (b) determining whether acoustic methods, together with other measurements and ocean modeling, can yield estimates of the time-evolving ocean state useful for making improved acoustic predictions, (c) improving our understanding of the physics of scattering by internal waves and spice, (d) characterizing the depth dependence and temporal variability of ambient noise, and (e) understanding the relationship between the acoustic field in the water column and the seismic field in the seafloor. In these experiments, moored and ship-suspended low-frequency acoustic sources transmitted to a newly developed distributed vertical line array receiver capable of spanning the water column in the deep ocean. The acoustic transmissions and ambient noise were also recorded by a towed hydrophone array, by acoustic Seagliders, and by ocean bottom seismometers.

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.

Tools for assessing conceptual understanding in the engineering sciences

One of the hindrances to reform in science, technology, engineering and mathematics (STEM) education is the absence of good assessment instruments that can measure the value added to student learning by new ways of teaching important material. The well-known Force Concept Inventory (FCI) assessment instrument is a good model of an instrument that can be used to check on students understanding of basic concepts in a discipline. This panel session paper discusses work in progress by the panel members and their co-developers to construct FCI-like Concept Inventories in each of the disciplines of thermodynamics, systems and signals, strength of materials, electromagnetics, circuits, materials, fluid mechanics, and transport processes.

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.

Students' interpretation of the importance and difficulty of concepts in signals and systems

Two ongoing challenges facing instructors when designing courses are (1) do students identify/understand important concepts in the course, and (2) what makes concepts difficult for students to understand? In particular, do students see the relationship between the procedures taught and the fundamental concepts they support? In this study, we use interviews with 39 undergraduate engineering students to address these questions in the context of a sophomore-level continuous-time signals and systems course. Each student interviewed was asked which concept in the course was most difficult, which was most important, and why. Student responses regarding the concepts and the reasons were qualitatively analyzed, and a codebook was developed. The results of the coding provide broad insight into what factors make a particular concept difficult and/or important from the student perspective. We conjecture that general elements drawn from the results obtained here can be applied beyond signals and systems and across the engineering curriculum.