Some of the factors involved in the design of a radar pulse compression system are discussed. These include the compression ratio, the detailed characteristics of the signal, the sidelobe level of the receiver output waveform (signal autocorrelation function), the sensitivity of the sidelobe level to Doppler frequency shift in the signal, and the relative complexity of the equipment required to generate and receive the signal. A signal of Gaussian envelope and linear frequency modulation is shown to have an autocorrelation function of Gaussian shape. When the receiver is designed to autocorrelate the linear FM Gaussian signal, it is shown that the shape of the receiver output waveform does not change when the input signal has a Doppler frequency shift. The design and construction of equipment used to generate and receive the signal are discussed. In operating equipment with a compression ratio of about 50 to one, sidelobe levels 40 db below the peak amplitude of the receiver output waveform are achieved, and the shape of the receiver output waveform does not change appreciably until the Doppler frequency shift exceeds 25 per cent of the 3-db signal bandwidth.