A method for amplitude modulated sinusoidal audio coding is presented that has low complexity and low delay. This is based on a sub-band processing system, where, in each subband, the signal is modeled as an amplitude modulated sum of sinusoids. The envelopes are estimated using frequency-domain linear prediction and the prediction coefficients are quantized. As a proof of concept, we evaluate different configurations in a subjective listening test, and this shows that the proposed method offers significant improvements in sinusoidal coding. Furthermore, the properties of the frequency-domain linear prediction-based envelope estimator are analyzed