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In this paper, an integrated cubic phase function (ICPF) is introduced for the estimation and detection of linear frequency-modulated (LFM) signals. The ICPF extends the standard cubic phase function (CPF) to handle cases involving low signal-to-noise ratio (SNR) and multi-component LFM signals. The asymptotic mean squared error (MSE) of an ICPF-based estimator as well as the output SNR of an ICPF-based detector are derived in closed form and verified by computer simulation. Comparison with several existing approaches is also included, which shows that the ICPF serves as a good candidate for LFM signal analysis.