Applying a Hadamard transform multiplexing scheme to an ion-mobility mass spectrometer improves the signal-to-noise ratio and duty cycle of the instrument. However, minor perturbations in the convolved data that do not perfectly align with the pseudo-random sequence (PRS) used to decode the data will cause periodic “echo” artifacts that lower the signal-to-noise ratio (SNR) and appear as noise in downstream processing of the data. A novel, general deterministic numerical analysis algorithm that discovers and eliminates periodic data artifacts based on knowledge of the deconvolution of the PRS has been developed that boosts the SNR. Any instrument that utilizes simplex matrices and the Hadamard transform can utilize this technique. This study determined that incorrectly decoded data exhibits a type of periodic symmetry about an axis of reflection corresponding to the encoding PRS, which the algorithm can utilize to remove the data artifacts. Knowledge of the true signal peaks that is derived from the encoded data allows for both artifacts and noise to be removed with high confidence, decreasing the likelihood of false identifications in subsequent data processing.