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This work came directly out of work done during the War on radar and control systems. Yet the radar work itself was an outgrowth of work beginning circa 1920 on improving the performance of communication systems in the presence of noise. We have previously reported on work carried out in this area during the 1920s in both radio (wireless) communications and wired telephony . In this paper we focus on work done in the 1930s and early 1940s, which both enlarged on, and saw considerable strides ahead in, these earlier studies involving noise in communication systems. We do this by presenting developments during this period of time in three inter-related, and roughly chronological, areas: 1. Work by Armstrong on FM and Reeves on PCM showing, for the first time, that noise could be reduced by purposefully increasing the bandwidth (now known as the noise-bandwidth tradeoff). This work is discussed in the next section covering the period of the 1930s. 2. Studies attempting to understand the statistical properties of noise, leading to its now-well-known Gaussian amplitude characteristic. This work is described in the section covering the late 1930s to early 1940s. 3. The recognition that ldquomatched filteringrdquo provided optimum signal detection in noise. This work, described in the last section of this paper, arose out of the need during World War II to detect small, pulsed, radar signals in the presence of noise.