The high acceleration of moving targets has brought severe problems in radar signal processing, such as the decrease in output signal-noise-ratio and the deterioration of Doppler resolution. This paper presents an acceleration ambiguity function (AAF) for characterizing the acceleration effects and the acceleration resolution property in radar signal processing. The definition of the acceleration resolution based on AAF is also presented. Using AAF as an analyzing tool, some factors are derived including the loss factor of output SNR, the broadening factor of Doppler resolution, and the optimal accumulative time (OPT) caused by acceleration in linear-phase matched filtering. The convergent property of quadratic-phase matched-filter for searching for and estimating the acceleration is discussed. The results and conclusions are helpful for the quantitative analysis of the acceleration effects on signal processing, and for evaluation of the performance of acceleration in radar signal waveform design. The high acceleration of moving targets has brought severe problems in radar signal processing, such as the decrease in output signal-noise-ratio and the deterioration of Doppler resolution. This paper presents an acceleration ambiguity function (AAF) for characterizing the acceleration effects and the acceleration resolution property in radar signal processing. The definition of the acceleration resolution based on AAF is also presented. Using AAF as an analyzing tool, some factors are derived including the loss factor of output SNR, the broadening factor of Doppler resolution, and the optimal accumulative time (OPT) caused by acceleration in linear-phase matched filtering. The convergent property of quadratic-phase matched-filter for searching for and estimating the acceleration is discussed. The results and related are helpful for the quantitative analysis of the acceleration effects on signal processing, and for evaluation of the performance of acceleration in radar signal wav eform design.