Optimum bit allocation for instantaneous floating point digitizers

An Instantaneous Floating Point (IFP) digitizer consists of an analog to digital converter preceded by a gain ranging amplifier and sampler. IFP digitizers are commonly used to record non-stationary signals corrupted by non-stationary noise, the signal plus noise having a large dynamic range. Statistical analysis for an arbitrary number of converter bits, number of gain bits, and gain base reveal the undesirable effects an IFP digitizer may produce. Relationships are obtained between the number of converter bits, number of gain bits, and gain base which, when satisfied, avoid these undesirable effects and cause the IFP digitizer to perform essentially as a sampler. Further application of these relationships produces a solution to the problem of finding the minimum total number of bits and their allocation between the converter and gain words.