False Alarm Rate and False Alarm Number for Discrete and Continuous Time Sampling

A comparison of the false alarm rates and false alarm numbers for discrete and continuous time sampling is given for different noise spectrums (rectangular, Hamming, Gaussian, and cosine noise voltage spectrums) and for different sampling rates for the case of discrete time sampling. Also given is the increase in the false alarm rate when going from discrete to continuous time sampling when the detection threshold is held fixed. The amount that the threshold has to be increased for continuous sampling to achieve the same false alarm rate obtained with discrete time sampling is also given.