A novel and improved apparatus for encoding a signal which is bursty in nature. In a code excited linear prediction algorithm, short term redundancies and long term redundancies are removed from digitally sampled speech, and the residual signal which is bursty in nature must be encoded. The residual signal is encoded using three parameters a burst shape index corresponding to a burst shape in a codebook of burst shapes, a burst gain, and a burst location. Together the three parameters specify a waveform to match the residual signal. Further disclosed is a closed loop exhaustive search method by which to find the best match to the residual waveform and a partially open loop method wherein the burst location is determined by an open loop analysis of the residual waveform, and the burst shape and gain parameters are determined in a closed loop fashion. Also disclosed are methods by which a burst vector codebook may be provided which may result in reduced computational complexity in the search algorithms including a recursive burst codebook and a codebook structured in such a way that members of the codebook are linear combinations of other members of the codebook.