The temporal Talbot effect (TTE) embodies the phenomenon of discrete Fourier transform (DFT). However, in an ideal temporal Talbot system, an infinitely long pulse train is required as input, which hinders the application of this property in optical computation of DFT. In this paper, we investigate the phenomenon of DFT in the TTE with input pulse trains of finite duration, aiming to apply it to optical computation of DFT. It is found that precise DFT coefficients can be extracted from the output signal of a system with an input pulse train of finite duration, subject to a specific condition on the pulse train’s duration. A significant advantage of the system employing an input pulse train of finite duration is that the resulting output signal becomes band-limited. This crucially implies that an optical receiver with a limited bandwidth can be utilized to obtain a distortionless signal. We provide a concise and rigorous theoretical framework on the TTE-based DFT system, which fully explains the underlying mechanism for perfect DFT calculation and is consistent with simulation results. Furthermore, we have determined that the single-cycle DFT calculation, using an input pulse train of one period, is feasible. The performance of the single-cycle DFT has been systematically evaluated under various non-ideal conditions, such as sampling time jitter and limited detection bandwidth. This research establishes a foundation for future applications of TTE in optical DFT computation, as it removes the requirement of inputting infinitely long pulse trains.

时间塔尔博特效应（TTE）体现了离散傅立叶变换（DFT）现象。然而，在理想的时态Talbot系统中，需要无限长的脉冲序列作为输入，这阻碍了该特性在DFT光学计算中的应用。在本文中，我们研究了具有有限持续时间的输入脉冲序列的TTE中的DFT现象，旨在将其应用于DFT的光学计算。研究发现，在脉冲序列持续时间的特定条件下，可以从具有有限持续时间的输入脉冲序列的系统的输出信号中提取精确的 DFT 系数。采用有限持续时间的输入脉冲串的系统的一个显着优点是所得输出信号变得带限。这至关重要地意味着可以利用带宽有限的光接收器来获得无失真信号。我们对基于TTE的DFT系统提供了简洁而严谨的理论框架，充分解释了完美DFT计算的底层机制，并且与仿真结果一致。此外，我们还确定使用一个周期的输入脉冲串进行单周期 DFT 计算是可行的。单周期 DFT 的性能在各种非理想条件下进行了系统评估，例如采样时间抖动和有限的检测带宽。这项研究为 TTE 在光学 DFT 计算中的未来应用奠定了基础，因为它消除了输入无限长脉冲序列的要求。