A method of producing at least one possible sequence of vocal tract resonance (VTR) for a fixed sequence of phonetic units, and producing the acoustic observation probability by integrating over such distributions is provided. The method includes identifying a sequence of target distributions for a VTR sequence corresponding to a phone sequence with a given segmentation. The sequence of target distributions is applied to a finite impulse response filter to produce distributions for possible VTR trajectories. Then these distributions are applied to a linearized nonlinear function to produce the acoustic observation probability for the given sequence of phonetic units. This acoustic observation probability is used for phonetic recognition.