Drift tube-ion mobility spectrometers (DT-IMSs) are used to separate and characterize the structures of gas phase ions. Recent work in coupling an atmospheric pressure DT-IMS to a condensation particle counter (CPC) has extended the application of drift tube ion mobility spectrometry to nanoparticle analysis, with measurements possible for singly charged particles up to 20 nm in diameter. In examining systems with such large analytes, often of interest is not only separation, but also determination of the nanoparticle size or mobility distribution function, defined as the nanoparticle concentration per unit mobility/size. Distribution function determination requires a priori knowledge of the DT-IMS transfer function, i.e. the DT-IMS combined transmission and detection efficiency as a function of both mobility and drift/arrival time. The transfer function completely describes analyte transport through an instrument; unfortunately, it has not been experimentally determined in previous work for a DT-IMS. Here, we develop and apply a new method to infer the transfer function of a DT-IMS-CPC system, wherein the system is used to measure particles which are first transmitted through a well-characterized differential mobility analyzer (DMA). The DMA acts as a mobility filter, and only transmits particles within a narrow, well-defined mobility range. From a series of measurements at fixed drift/arrival time (up to 12 seconds) but variable DMA transmission window, DT-IMS-CPC transfer functions are inverted via a Twomey-Markowski algorithm. Transfer function inversion reveals that the DT-IMS-CPC system has a resolving power in excess of 10 and upwards of 20. Such resolving powers are in good agreement with model predictions, and are higher than commercially available DMAs in the nanoparticle size range.