Comments on "Optimum Bandwidth of a Low-Pass Filter for Detection of a Pulse in Nonstationary Noise"

In a recent correspondence1 a calculation of the optimum bandwidth of a low-pass RC filter for the detection of a pulse signal in nonstationary noise was presented. The purpose of this correspondence is: 1) to point out additional references to the work which has been conducted in the stationary noise case, and 2) to present an interesting alternate derivation of the expected output noise power for the nonstationary noise case.     

Noncoherent Detection of Sinusoidal Signals in Sinusoidal Clutter

Probability density expressions associated with the noncoherent detection of a sinusoidal signal have been obtained. The signal is assumed to be imbedded in sinusoidal clutter at the same frequency and narrow-band Gaussian noise. The density expressions are shown to be a function of the signal-to-noise power ratio and the clutter-to-noise power ratio. The expressions have been numerically evaluated for a number of conditions, and the results under each reception hypothesis are presented graphically. Under large-sample conditions, the probability density for a multisample test statistic is shown to be Gaussian, and the probability of detection expression is written such that commonly available tabulated data can be utilized to determine the probabilities.