Nonlinear acoustic signals, specifically the parametric effect, offer significant advantages over linear signals because the low frequencies generated in the medium due to the intermodulation of the emitted frequencies are highly directional and can propagate over long distances. Due to these characteristics, a detailed analysis of these signals is necessary to accurately estimate the Time of Arrival (ToA) and amplitude parameters. This is crucial for various communication applications, such as sonar and underwater location systems. The research addresses a notable gap in the literature regarding comparative methods for analyzing nonlinear acoustic signals, particularly focusing on ToA estimation and amplitude parameterization. Two types of nonlinear modulations are examined: parametric Frequency-Shift Keying (FSK) and parametric sine-sweep modulation, which correspond to narrowband and broadband signals, respectively. The first study evaluates three ToA estimation methods—threshold, power variation (Pvar), and cross-correlation methods for the modulations in question. Following ToA estimation, the amplitude of the received signals is analyzed using acoustic signal processing techniques such as time-domain, frequency-domain, and cross-correlation methods. The practical application is validated through controlled laboratory experiments, which confirm the robustness and effectiveness of the existing methods proposed under study for nonlinear (parametric) acoustic signals.