Scharf, Louis L., authorVoran, Stephen D., authorIEEE, publisher2007-01-032007-01-031994Voran, Stephen D. and Louis L. Scharf, Polar Coordinate Quantizers That Minimize Mean-Squared Error, IEEE Transactions on Signal Processing 42, no. 6 (June 1994): 1559-1563.http://hdl.handle.net/10217/741A quantizer for complex data is defined by a partition of the complex plane and a representation point associated with each cell of the partition. A polar coordinate quantizer independently quantizes the magnitude and phase angle of complex data. We derive design equations for minimum mean-squared error polar coordinate quantizers and report some interesting theoretical results on their performance, including performance limits for "phase-only" representations. The results provide a concrete example of a biased estimator whose mean-squared error is smaller than that of any unbiased estimator. Quantizer design examples show the relative importance of magnitude and phase encoding.born digitalarticleseng©1994 IEEE.Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.encodingapproximation theoryanalogue-digital conversionText