US Patent 7424380 Method and apparatus for integrated distribution function capture

Probability distribution functions (PDFs), of a periodic input data signal, can be used to provide eye-diagram information. An advantage of PDFs, over conventional approaches to eye-diagram collection, is that analog-to-digital conversion can be accomplished by the slicer of a receiver, provided the slicer can programmably change its threshold. A cumulative distribution function (CDF), at a particular phase of a desired eye-diagram, can be collected by having a receiver's slicer scan its threshold level. For each threshold level, a fixed number of symbols can be analyzed as follows to produce a CDF value: count the number of times a particular symbol value occurs. The derivative of a CDF can produce its PDF, where each PDF can represent a “slice” of a desired eye-diagram. For a non-periodic input signal, an eye diagram can still be formed so long as the percentage occurrence, of each symbol value, remains at least approximately the same.