Allpass-Based Chirp Design With Perfect Pulse Compression Property

Abstract

Chirp waveforms are widely used in radar, sonar, acoustics, and other sensing systems due to their desirable pulse-compression behavior. However, standard chirp signals like linear frequency modulation (LFM) waveforms inevitably produce sidelobes that limit detection performance. In this paper, we propose a unified allpass-based chirp design (ABCD) framework that generates chirp-like waveforms with the perfect pulse compression (PPC) property, i.e., their autocorrelation reduces exactly to an impulse. The key idea is to design an allpass IIR system whose impulse response resembles a chirp. The allpass structure guarantees zero sidelobes, while its phase response closely approximates the ideal LFM. Band-limited chirp waveforms and long-duration, high–time-bandwidth signals can be obtained via interpolation and cascading, while preserving the perfect pulse-compression property. Compared with existing windowing or nonlinear FM techniques, the proposed method achieves exact sidelobe elimination together with flexible control of waveform characteristics, offering clear advantages for high-resolution and high–dynamic range sensing applications.