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We present a technique for applying arbitrary invertible nonlinear functions to the internal signals of a prototype linear time-invariant digital signal processor, without causing any output disturbances. By using our proposed technique, the external input-output behavior of the DSP remains linear, and identical to that of the prototype, despite the nonlinear behavior of its internal signals. We explore the specific application of our technique to instantaneous companding, in which the introduced nonlinearities compress the dynamic range of the internal signals, so that the latter span most of the available bits in the system, thus improving the signal-to-noise-plus-distortion-ratio at the output, for low to medium input signal levels. We discuss the choice of nonlinear functions for this companding application, and we present an efficient hardware implementation for the standard 15-segment piecewise-linear approximation to the 255-μ law. We compare the performance and hardware overhead of our technique with that of other companding architectures.