Quadratic detectors for energy estimation

The estimation of signal energy is an important part of physics and signal processing. A commonly used energy estimate in signal processing is instantaneous energy that is defined by the square of the signal magnitude at time t, i.e., |x(t)|². For a noisy signal, a standard energy detector, which consists of a linear time-invariant (LTI) filter followed by a magnitude-squared operator, is commonly used to reduce noise and extract signal energy in a certain frequency band. However, due to the temporal response of the LTI filtering, this energy estimate is smeared in time. In addition, it is unclear how this estimate relates to the physical energy in the system that produced the signal. e propose simple quadratic systems producing frequency-selective energy estimates and effective noise reduction with little or no smearing in time. We introduce the new concept of quadratic detectors, discuss desirable time and frequency resolution properties of a general quadratic detector, and study five different applications to demonstrate the simplicity of quadratic detector design and implementation