In this paper, we generalize the standard blockwise linear predictive (LP) coding by introducing low-pass filtering and downsampling of the LPC vectors at the encoder side, accompanied by interpolation at the decoder. Several concepts in LP coding, such as overlapping frames, interpolation and long analysis frames, can be described in the proposed framework. We also note that the proposed methods are in agreement with previous work on spectral dynamics, which indicates that spectral dynamics is (at least) as important as spectral distortion for speech quality. We have applied the proposed method to low-rate quantization of spectrum parameters. Objective and subjective performance of the new approach is compared to a standard blockwise LP coding, at various rates. We show that both the subjective and objective quality of the new method compare favorably with standard methods. Even at as low rate as 500 bit/s, the proposed method has a good quality.