The relationship between spectrum and PEF

Knowledge of an autocorrelation function is equivalent to knowledge of a spectrum. The two are simply related by Fourier transform. A spectrum or an autocorrelation function encapsulates an important characteristic of a signal or an image. Generally the spectrum changes slowly from place to place although it could change rapidly. Of all the assumptions we could make to fill empty bins, one that people usually find easiest to agree with is that the spectrum should be the same in the empty-bin regions as where bins are filled. In practice we deal with neither the spectrum nor its autocorrelation but with a third object. This third object is easily transformed to the spectrum. This third object is the Prediction Error Filter (PEF). Its spectrum is inverse to the data spectrum.