1. A signal processing apparatus configured to encode audio data signals for data communications comprising: a processor; an input coupled to the processor configured to receive an audio signal to be processed; range calculation means for determining a range that includes an input value corresponding to the received audio signal and for providing a predetermined discrete value representative of the input value, wherein the predetermined discrete value is obtained by discretizing a computation result of a nonlinear operation; discrete value output means for outputting the predetermined discrete value to a residual signal calculator; summation order determining means for determining a summation order to be used by the residual signal calculator based upon an inverse quantized value of the predetermined discrete value; and the residual signal calculator configured to calculate a residual signal based upon spectrum data of the received audio signal, the determined summation order, and at least one linear predicted coefficient that is based at least in part on the predetermined discrete value.