In response to the severe challenges posed to data acquisition systems by the complex characteristics of modern electronic warfare and communication signals, such as wide bandwidth, strong transients, and high dynamic range, this paper designs and implements a bandwidth high-speed data acquisition system with a sampling rate of 40 GSPS and a bandwidth of 18 GHz. Meanwhile, to address the offset, gain, and phase mismatches introduced by the multi-core parallel interleaved architecture of ultra-high-speed time-interleaved analog-to-digital converter (TI-ADCs), an error correction method based on the adaptive moment estimation (ADAM) optimizer is proposed. By incorporating first-moment estimation and second-moment adaptive adjustment, the proposed method dynamically regulates the parameter update step size during the correction process. This mechanism effectively mitigates the limitations of traditional fixed-step-size algorithms, which are susceptible to gradient vanishing or local optima when dealing with complex non-stationary errors, thereby achieving adaptive rapid convergence and high-precision optimization of the correction parameters. Consequently, rapid convergence and high-precision optimization of the correction parameters can be achieved. Measurement results from a hardware verification platform demonstrate that, over the full Nyquist operating bandwidth from direct current (DC) to 18 GHz, the corrected system achieves an signal-to-noise ratio (SNR) improvement of 20.0 to 23.7 dB and an spurious-free dynamic range (SFDR) improvement of 16.4 to 22.0 dBc. Compared with the traditional least mean square (LMS) algorithm, the proposed method effectively suppresses the periodic oscillations that may occur under the influence of complex nonlinear errors, reducing the number of convergence iterations to fewer than 66 while maintaining the steady-state residual within a low range of 0.472 to 0.491. The results demonstrate that the proposed broadband high-speed system and correction method successfully balance convergence speed, steady-state correction accuracy, and enhanced broadband dynamic performance, thereby providing an effective implementation solution for the high-precision, real-time acquisition of broadband signals in complex environments.