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Classical work in the field of high-resolution radar often assumes that an echo signal is made of a number of components that can be decomposed via Fourier analysis. Adjacent components are said to be resolved in the frequency domain if the intensity between them drops at least 3 decibels. This working definition is an extension of Lord Rayleigh's criterion for optical resolution. The problem with this approach is that whereas Rayleigh's criterion assumes signal incoherence, thus allowing for the addition of power components, a high-resolution radar signal is often the coherent sum of sinusoids, which implies voltage addition. The purpose of this paper is to discuss the consequences of using Rayleigh's criterion in the analysis of radar signals. Specifically, computer simulations using a complex signal are analyzed via the periodogram as the relative phase between the two components of the signal is allowed to change. The net effect introduced by this phase variation is to reduce or increase the spacing and intensity between two adjacent spectral peaks. These changes are due to constructive or destructive interference of spectral cross terms that cannot be ignored when attempting to resolve frequency components from one another. For instance, the simulations show that when using the averaged periodogram, the intensity in-between two adjacent components is above the -3 decibel threshold for a phase range of 1.2π radians, although the standard resolution criterion of c/2β is satisfied. Similar results are obtained when using a number of windows that are known to control sidelobe levels. Thus, the use of Rayleigh's criterion to define the resolution of a high-resolution radar system is technically inconsistent and undermines our ability to perform quantitative comparisons of target profiles, Doppler profiles and range-Doppler images. In this light, the authors promote the adoption of alternative criteria for judging resolution gains based on the norm of the signal in the (spatial) frequency domain.
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