This paper describes the design of a candidate noise processor for the Sanguine receiver based on communication theory considerations and detailed experiments using wide-band recordings of extremely low-frequency (ELF) (3-300 Hz) atmospheric noise. This processor consists of the following elements: 1) a compensating (or whitening) filter; 2) nonlinear notch filtering at frequencies of manmade interference; 3) a post-notch filter nonlinearity; and 4) a phase coherent linear matched filter. Due to the impulsive non-Gaussian nature of the noise, nonlinear processing with a bandwidth considerably greater than the 40-80-Hz signal bandwidth is significantly better than a linear receiver (consisting only of a matched filter and appropriate whitening filters). Simulations using noise recordings from a number of widely separated locations in the world have shown improvements of 7 dB to 20 dB at times of high ELF atmospheric noise levels at the receiver input.