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In this work, the pulsation analysis is performed on 83 high-amplitude $\delta$ Scuti stars, which have been observed by the Transiting Exoplanet Survey Satellite (TESS). The results show that 49 of these HADS show single-mode pulsation, 27 of them show radial double-modes pulsation (in which 22 of them pulsate with the fundamental and first overtone modes and 5 of them pulsate with the first and second overtone modes), and 7 of them show radial triple-modes pulsation (3 of which are newly confirmed triple-mode HADS). The histogram of the fundamental periods and the ratios between the fundamental and first overtone periods show bimodal structures, which might be caused by the stellar evolution in this specific phase. Most of the radial triple-mode HADS have a fundamental amplitude of 41-54 mmag, and 50% of them have similar amplitudes of the fundamental and first overtone pulsation modes. All these hints require further confirmation not only in observations with more HADS samples, but also in theoretical models with suitable treatments of stellar evolution and pulsation., Comment: 11 pages, 8 figures, 3 tables. RAA published