Signal comparison is one of the most basic operations in seismic imaging and data processing. We normally implement such a comparison in the framework of the linear signal analysis such as the crosscorrelation. However, this linear signal comparison (LSC) has an inherent drawback in that the time or space sensitivity and resolution is poor for low frequency signals. To overcome this limitation, we propose a new nonlinear signal comparison (NLSC) approach where we can obtain a uniform resolution across a frequency band. We can control the overall resolution in NLSC over the frequency band by an adjustable parameter. The traditional crosscorrelation is a special case corresponding to one value of the parameter. We demonstrate the effectiveness of NLSC by extracting surface Rayleigh wave dispersion curves from 5 different datasets, including a synthetic fundamental-mode Rayleigh wave data, synthetic overtone Rayleigh waves, synthetic global Rayleigh waves of a Martian seismic model which is useful for the future Martian seismological mission, an exploration-type seismic gather generated by a dynamite source, and a real ambient noise correlation data processed from the USArray. We observe that over a wide range of frequencies, the NLSC method can achieve high-fidelity extraction of the dispersion curve in particular at the low frequency end.