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Delay alignment modulation (DAM) is a promising technology to achieve ISI-free wideband communication, by leveraging delay compensation and path-based beamforming, rather than the conventional channel equalization or multi-carrier transmission. In particular, when there exist a few strong time-dispersive channel paths, DAM can effectively align different propagation delays and achieve their constructive superposition, thus especially appealing for intelligent reflecting surfaces (IRSs)-aided communications with controllable multi-paths. In this paper, we apply DAM to multi-IRS aided wideband communication and study its practical design and achievable performance. We first provide an asymptotic analysis showing that when the number of base station (BS) antennas is much larger than that of IRSs, an ISI-free channel can be established with appropriate delay pre-compensation and the simple path-based MRT beamforming. We then consider the general system setup and study the problem of joint path-based beamforming and phase shifts design for DAM transmission, by considering the three classical beamforming techniques on a per-path basis, namely the low-complexity path-based MRT beamforming, the path-based ZF beamforming for ISI-free DAM communication, and the optimal path-based MMSE beamforming. As a comparison, OFDM-based multi-IRS aided communication is considered. Simulation results demonstrate that DAM outperforms OFDM in terms of spectral efficiency, BER, and PAPR.