In this paper, an effective speech coder that is based on a sparse representation of speech by exploiting the strong dependencies between adjacent pitch cycles is proposed. In the proposed coder, a pitch-synchronous processing that consists of pitch warping and a two-stage transformation is used to achieve a compact representation of the voiced speech. Power spectral density preserving quantization (PSD-PQ) is adopted for quantizing the transform coefficients. The result is a coder that is efficient over a wide range of bit rates: it approaches perfect reconstruction with increasing rate, and has a parametric signal representation at low rates. Both objective PESQ results and subjective A/B listening tests show that the proposed coder outperforms the ITU-T G.722.1 codec.