It may be demonstrated that interpolating, on a sample-by-sample basis, the short-term spectral envelope parameters at both the analysis and synthesis stages of a low-bit rate speech coder can significantly improve the decoded speech quality. Results obtained using two alternative short-term spectral representations are compared, i.e. Linear Prediction (LP) filter coefficients and Line Spectral Frequencies (LSF's). LSF's have the advantage of preserving the stability of the synthesis filter throughout the interpolation process and lower computational complexity. The representations have been compared for a PWI coder and objective measurements and informal listening tests have shown that marginally better subjective performance is obtained from the computationally simpler LSF interpolation process. An interpolated LSF synthesis filter has been implemented in a CELP coder. About 0.4 dB improvement in the SNR measure was obtained as compared with a conventional blockwise interpolated CELP coder.