Generalized Regular Sampling of Trigonometric Polynomials and Optimal Sensor Arrangement

• Main Authors: Goyal, Vivek K. (Contributor), Deshpande, Ajay A. (Contributor), Sarma, Sanjay E (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Mechanical Engineering (Contributor), Massachusetts Institute of Technology. Laboratory for Electromagnetic and Electronic Systems (Contributor), Massachusetts Institute of Technology. Laboratory for Manufacturing and Productivity (Contributor), Massachusetts Institute of Technology. Research Laboratory of Electronics (Contributor), Sarma, Sanjay Emani (Contributor)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers (IEEE), 2012-04-05T17:04:03Z.
• Subjects: Article
• Online Access: Get fulltext

We address the optimal sensor arrangement problem, which is the determination of a geometric configuration of sensors such that the mean-squared error (MSE) in the estimation of an unknown trigonometric polynomial is minimum. Unsurprisingly, an arrangement in which sensors are spaced uniformly in each dimension is optimal. However, for multidimensional problems the minimum MSE is achieved with a much larger class of configurations that we call generalized regular arrangements. These arrangements are not necessarily generated by lattices and may exhibit great nonuniformity locally.