1960/03/01 by J. Max · 2,066 citations
Computer Science · Engineering · Mathematics · #Advanced Data Compression Techniques #Algorithm #Amplitude distortion #Computer science #Control theory (sociology) #Distortion (music) #Function (biology) #Image and Signal Denoising Methods #Mathematical optimization #Mathematics #Measure (data warehouse) #Minification #Nonlinear distortion #SIGNAL (programming language) #Sparse and Compressive Sensing Techniques #Telecommunications
paper · doi:10.1109/tit.1960.1057548
published in IEEE Transactions on Information Theory 6(1), 7-12 (Institute of Electrical and Electronics Engineers)
openalex publication_date 1960/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
This paper discusses the problem of the minimization of the distortion of a signal by a quantizer when the number of output levels of the quantizer is fixed. The distortion is defined as the expected value of some function of the error between the input and the output of the quantizer. Equations are derived for the parameters of a quantizer with minimum distortion. The equations are not soluble without recourse to numerical methods, so an algorithm is developed to simplify their numerical solution. The case of an input signal with normally distributed amplitude and an expected squared error distortion measure is explicitly computed and values of the optimum quantizer parameters are tabulated. The optimization of a quantizer subject to the restriction that both input and output levels be equally spaced is also treated, and appropriate parameters are tabulated for the same case as above.