Comprehensive emissions models extensively use engine exhaust data from vehicle experiments to represent the relationship between fuel composition and pollutants. However, the predicted emissions from these models often neglect the effects of transients and speed-load history. Fourier transform infrared (FTIR) spectroscopy is a high frequency measurement technique capable of comprehensive speciation. However, due to long residence times of exhaust within a FTIR spectrometer gas cell, FTIR measurements are contaminated by the effects of historical emissions, precluding the attainment of time-resolved engine exhaust data. This work presents a Bayesian estimation model for processing FTIR measurements to obtain accurate estimations of instantaneous engine exhaust composition. The Bayesian model utilizes a simple model of the mixing dynamics of the gas cell and measurement noise statistics to estimate the composition of exhaust entering the FTIR gas cell during a measurement period. To validate the estimation model, synthetic FTIR measurements are generated from simulated engine exhaust data from the Federal Test Procedure driving cycle. These synthetic measurements are processed by the estimation model, which is shown to yield improved estimations of instantaneous composition as compared to the raw FTIR measurements, although the degree of improvement depends on the magnitude of measurement noise and flow rate through the FTIR gas cell. For a measurement noise standard deviation of 0.5% of the maximum measurement, the estimation model improved estimates of instantaneous NO emission by approximately 42.5% on average, while about a 7.5% improvement was achieved for a measurement noise standard deviation of 2% of the maximum measurement for a FTIR flow rate of 10 L/min. For a flow rate of 25 L/min, improvements of approximately 41.5% and 6% were achieved for measurement noise standard deviations of 0.5% and 2% of the maximum measurements, respectively. The application of the model in this work is to generate time-resolved emissions estimates to further elucidate the relationship between fuel composition and engine emissions.