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In low rate speech coders, frame-based speech spectral parameters, represented by line spectral frequencies (LSF), are typically encoded by vector quantization without exploiting explicitly the temporal correlation between frames. Recently, however, methods have been proposed that model the temporal trajectory of each LSF over a speech segment by a low-order polynomial function. In the present work, we propose a method that exploits the joint spectro-temporal correlation across a speech segment. The LSF values are treated as points on a smooth surface obtained by fitting a low-order bivariate polynomial function of the variables, frame index and LSF index. The issues that arise in incorporating such joint modeling in a low bit rate coder are identified, and some comparative results of performance are presented.