Single-sideband (SSB) and AM signals are analyzed using a waveform that can be varied in shape from a spike through a sine wave to a square wave by varying a parameter. The average sideband powers and the peak envelope powers are then calculated and compared. It is shown that the ratio of average sideband power to peak envelope power for AM is more favorable than that for SSB for 'squarish' modulating signals. However, the ratio for SSB is about 9 dB higher than it is for AM for modulating signals ranging in shape from a sine wave to a spike.>

An analysis of the effect of hard limiting on a sum of three or four sinusoidal signals has been performed. Analytic expressions are obtained for the output amplitudes for three input signals, two of equal amplitude, and for four signals, amplitudes equal in pairs. The results are compared with previous investigations that employ digital computer simulation, and excellent agreement is obtained. The signal suppression is investigated, and the "negative suppression" effect found numerically by other authors is shown to arise from logarithmic terms in the dependence of the output amplitude on the input signal amplitude ratio. These results should aid in understanding the interactions that occur when a limiting communications receiver is addressed by several signals.

In a coherent search rader, the pulse-to-pulse Doppler shift of a signal is generally not known a priori. Given the distribution of this parameter, the best test variable for detection is the average of the likelihood ratio with respect to target Doppler frequency. Most coherent search radars employ a maximum-likelihood ratio detector, that is, a bank of independent Doppler filters, for detection. The average-likelihood and maximum-likelihood tests are compared here for a target with the Rayleigh amplitude distribution. It is shown that, over a wide range of detection and false-alarm probabilities, the performances of the two tests do not differ significantly. For this target model, the likelihood ratio has the Pareto distribution, which arises in some statistical problems in economics. The new results obtained here for the distribution of the sum of two or more Pareto-distributed variables are of considerable general interest.