Digital samples of an underlying analog audio-frequency signal are converted to transform coefficients and a first bit assignment value indicating the number of quantization levels or bits is adaptively assigned to each coefficient according to the power distribution of the transform coefficients. The transform coefficients are weighted according to a prescribed pattern such as human's auditory sensitivity, and a second bit assignment value is further adaptively assigned to each transform coefficient according to the power distribution of the weighted transform coefficients. One of the first and second bit assignment values is selected according to the power distribution of the transform coefficients and used to quantize the transform coefficients. The quantized transform coefficients are multiplexed with supplemental information derived from the transform coefficients for transmission to a receiving site. A process inverse to that at the transmitting site is performed on the multiplexed signal to recover the original digital samples.