We report rapid nanometer-scale chemical identification of polymer films using atomic force microscope infrared spectroscopy (AFM-IR). AFM-IR enables chemical characterization and identification in an AFM, but requires a relatively long acquisition time for high resolution mapping due to its low signal to noise ratio (SNR). In AFM-IR, infrared laser light incident upon a sample results in photothermal expansion of the sample, which is measured by an AFM tip in contact with the sample. The resulting cantilever vibrations vary in both time and frequency. We analyze the cantilever dynamic response during AFM-IR using a wavelet transform technique, which reveals how the energy is localized in the cantilever response. Based on this analysis, we tailor a time-frequency-domain filter to identify the region of highest vibrational energy. This approach can increase the SNR of the AFM-IR signal, such that the throughput is increased by 32X compared to state of the art. We show how this SNR improvement can improve AFM-IR imaging speed and chemical identification of nanometer-scale domains in polymer films.