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Maximum Entropy Signal Processing of Two-Dimensional NMR Data. J. Magn. , 64, 436-440. L. , 1990. Maximum Entropy Reconstruction of Complex (Phase Sensitive) Spectra. J. Magn. , 86, 236-246. W. , 1983. Comments and Correction to "Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum Cross-Entropy". 1EEE Trans. lnf. , IT-29(6), 942-943. , SkiUing, J. , 1985. Maximum Entropy Reconstruction of Spectra Containing Antiphase Peaks. J. Magn. , 63, 418-424. , Sibisi, S. , 1985.

For the 28 remainder of this chapter, 'information' will usually be employed in the physical sense: increasing information implies decreasing entropy S, and vice versa. Equation (2) gives the functional form of entropy S in terms of a probability distribution p. Shannon arrived at this formula by suggesting that entropy should satisfy a few simple conditions if it is to coincide with intuitive ideas of how an information measure should behave. These requirements, which may be stated in the form of four axioms, are as follows:(I) S should be a continuous function of the Pi.

_. ,==,%~ = ~'. ~ - == " = ~, '~-'- , - ~ - ~ . - - . /T or - 1/T spectnlm copy translated by 2/T Fig. 15 9Sampling outside of Nyquist condition (real part only)" the original spectnlm and its first copies (translated by I/T or -l/T) overlap. L r x FL ,,= = = x NM Id~ X M • ~ FT-i |'~ i i x=x= =IdMN~ j % x, t I/2T V Fig 16 9Aliasing (real part only). Peaks 1 and 2 belong to the original spectrum and peak 3 to its copy translated by I/T. As the spectrum is expected between frequencies -1/2T and I/2T, peak 3 is seen as peak 2 folded back around 1/2T.

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