Performance of spectral line detection using integrated trispectrum

The integrated trispectrum (IT) as an alternative to the delay and multiply (D&M) nonlinearity circuit is investigated. A spectral line detection/estimation scheme that employs the IT is developed. The conventional IT estimate utilizing the Fourier transform for relating a time signal to its frequency-domain representation is shown to be a major mathematical foundation for this analysis. The relation between the output power spectrum of the D&M circuit and the fourth moment spectrum of the input is established. The asymptotic performance for the detection probability is also analyzed. Simulation results provide the comparison between the IT approach and the standard D&M moment spectral method, and validate their theoretical performance bounds