An expression for the frequency spectrum of a digital radio frequency memory signal

A digital radio-frequency memory (DRFM) is an electronic countermeasures device that samples and quantizes (analog to digital conversion) an incoming radar signal and produces (digital to analog conversion) a jamming signal from the sampled radar signal. An equation for the frequency spectrum of a signal produced by a DRFM is derived. The derivation of the equation assumes that the incoming radar signal has a finite duration and a single frequency, that the ratio of the radar frequency (after heterodyning to baseband) to the sampling frequency is rational, and that the components used in the DRFM are ideal. The quantization of the sampled values causes harmonics in the DRFM signal. The magnitude of the harmonics is a major concern to the designers of DRFM systems, and an equation for predicting the magnitude of the harmonics is necessary for performance analysis. This equation provides an easy and fast method for determining how the magnitude of the harmonics is affected by the number of quantization levels (bits) in the analog-to-digital converter