Based on the extended Huygens-Fresnel principle, the analytical expression for the spectrum of ultrashort pulsed Hermite-Gaussian (H-G) beams propagating through the turbulent atmosphere is derived. The spectral shift and spectral transition are studied, and reasonable physical explanations are given. It is shown that the spectrum depends on the structure constant of the refractive index, order of the Hermite polynomial, pulse duration and position of the observation point. The on-axis spectrum is blue-shifted, the off-axis spectrum becomes red-shifted with increasing transverse coordinate, and the position with null spectral shift is independent of pulse duration. Furthermore, there exists an off-axis spectral transition when the turbulence reaches a certain degree. The behavior of the off-axis spectral transition in turbulence is very different from that in free space, which is analyzed in detail.
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