Array theory is widely utilized in applications involving wave phenomena, from sonar and radar to radio telescopes and medical imaging.  More recently, array theory has been extended to audio applications with the widespread adoption of line array loudspeaker systems and ongoing interest in microphone arrays.  This one-day course provides an introduction to array theory and a basic understanding of the signal processing methods used with acoustic transducer arrays.    

The course begins with a brief review of mathematical concepts used in array theory, followed by a discussion of idealized sound sources and receivers and basic properties of acoustic transducers.   The theory of acoustic arrays as a collection of discrete transducers is developed and properties of arrays are explored.  Array signal processing concepts such as beamforming and spatial filtering are derived and explained.  Example arrays are considered and optimization of array parameters for specific applications is demonstrated using PC-based simulations.   A brief introduction to more advanced topics may be included subject to participant interest. 

This course is intended as an introduction to Array Theory for engineers, programmers and others working on projects or systems involving acoustic transducer arrays.  Some familiarity or prior exposure to mathematical concepts used in array theory is assumed but not required.    

Topics :         

  • Introduction and Review
    • Complex exponential representation of acoustic waves; Fourier transforms
  • Characterization of Acoustic Transducers
    • monopole radiation; ideal (simple) sources and receivers; distributed sources
    • source level; axial response; directional response and beam patterns; directivity, directivity index; 
  • The Discrete Element Line Array
    • derivation of axial and directional acoustic fields; beam steering; array gain
    • array parameterization – aperture and element spacing, beam patterns and frequency response;
  • Array Signal Processing
    • Array shading; time domain beamforming; frequency (phase) domain beamforming; source angle estimation, source localization; energy detection; matched filter processing
    • Beam patterns and spatial filtering; spatial Fourier transform
  • Example arrays and applications
    • Wavenumber-to-size (ka) wavenumber-to-spacing (kd) and nearfield vs far field (kr) dependence
    • Array optimization ; array performance in realistic noise environments
    • Optional topics – adaptive beamforming; matched field processing; self-noise mitigation, other TBD

Dr. Chris Barber is the founder of Multipath Science and Engineering Solutions and has over twenty years’ experience in applied acoustic research ranging from acoustic testing of naval ships to characterization of professional audio systems.  He has taught courses and advised students in acoustics, audio and electrical engineering at the undergraduate, graduate and professional continuing education levels.

Course participants receive a hard copy of the instructor’s course notes and selected reference materials.  Following the course, opportunities are provided to schedule a web-based follow-up Q&A session between the instructor and course participants.  

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