Bounds on the Spectrum of a CHIRP Pulse

A simple method is described for calculating and plotting strong bounds on the frequency spectra of linear frequency modulated (LFM) pulses used in CHIRP radar transmitters. Bounds on the voltage density (amplitude), energy density, power density, or power spectrum can be hand calculated and plotted in 10 to 20 minutes with a computational accuracy that is adequate for most electromagnetic compatibility (EMC) analyses. The bounds obtained are within one dB of the peaks of the central lobe and major sidelobes. The method is based on the fact that the bounds on the far sidelobes are essentially the same whether or not the pulse is LFM. Several numerical examples are given for Hamming-weighted and trapezoidal pulses. The method is a convenient mathematical tool for engineers involved in compatibility analysis or concerned with radar transmitters complying with military standards pertaining to EMC.