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In our group we pursue two experimental approaches to investigate Intramolecular Vibrational Redistribution (IVR): this process can be studied by time-resolved femtosecond pump-probe experiments, or the corresponding time-dependent quantum dynamics can be obtained from stationary spectra in the IR at high frequency resolution by a time-dependent analysis using the underlying Hamiltonian and time evolution operator, J. Manz and L. Woeste, eds. Verlag Chemie (Weinheim, 1995).}. Recent work in our group \textbf{5337}, 178 (2004);V. Krylov, A. Kushnarenko, E. Miloglyadov, M. Quack, and G. Seyfang, \textit{Proc. SPIEE} \textbf{6460}, 64601D-1 (2007).} has shown that CH$3$I and its deuterated isotopomers have different IVR-times, revealing different intramolecular coupling schemes for the initially excited vibrational levels. The present work is part of a larger effort to understand IVR in these molecules on the basis of high resolution spectra in the 500-12000~cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ region. In previous work we have analyzed the strong Fermi-resonance coupling between the CH-stretching and bending modes in CHD$2$I at modest resolution, demonstrating very fast redistribution times on the order of 100~fs \textbf{106}, 1303 (2008).}. We refer to this recent paper for the past literature on the topic. Here we present detailed rovibrational analysis of $\nu 1$ and several other fundamentals of CHD$2$I recorded with our high resolution FTIR spectrometer Bruker ZP2001 \textbf{8}, 1271 (2007).} with resolutions up to 0.0008~cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. We discuss our new results in relation to our recent work on the overtone spectra and dynamics and to the femtosecond pump-probe results.