Frequency domain linear prediction (FDLP) uses autoregressive models to represent Hilbert envelopes of relatively long segments of speech/audio signals. Although the basic FDLP audio codec achieves good quality of the reconstructed signal at high bit-rates, there is a need for scaling to lower bit-rates without degrading the reconstruction quality. Here, we present a method for improving the compression efficiency of the FDLP codec by the application of the modified discrete cosine transform (MDCT) for encoding the FDLP residual signals. In the subjective and objective quality evaluations, the proposed FDLP codec provides competent quality of reconstructed signal compared to the state-of-the-art audio codecs for the 32 − 64 kbps range.