Signal-to-Noise Ratio Requirements for Half-Wave and Full-Wave Nonlinear Detectors with Arbitrary Power Laws, Sampling Rates, Input Spectra, and Filter Characteristics

摘要

The output signal-to-noise ratio of a signal detection system consisting of a sampler, a nonlinear rectifier, and a low-pass filter, is evaluated generally, for arbitrary half-wave or full-wave nu-th law rectifiers, sampling rates, input spectra, input signal-to-noise ratio, and filter characteristics. The usual assumption of a long averaging time, relative to the inverse bandwidth of the input spectrum, is not made, thereby affording an explanation of the anomalous behavior of a half-wave rectifier for low-Q input spectra. A pitfall of employing the long averaging time assumption is illustrated via numerical example. A simple recurrence for the half-wave and full-wave nu-th law rectifier coefficients allows for a very fast and efficient high-order series evaluation of the output signal-to-noise ration for any value of nu. For moderate-or-large-Q input spectra, the possibility of using deliberate undersampling with no loss of performance is illustrated. The use of a half-wave rectifier generally requires a higher sampling rate than does a symmetric full-wave rectifier; also the performance is somewhat poorer for the half-wave rectifier, and in some cases, significantly so.