Externally Linear Discrete-Time Systems With Application to Instantaneously Companding Digital Signal Processors

Abstract

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-law. We compare the performance and hardware overhead of our technique with that of other companding architectures.Index Terms-Companding systems, externally linear systems, internally nonlinear systems, fixed-point arithmetic, quantization.

Internally Non-LTI Systems Based on Delays, With Application to Companding Signal Processors

“…Consistent with the findings in [4], [6], and [7], no instability has been observed in this system; this is attributable to the fact that g(t) depends only on the input and does not introduce additional feedback paths.…”

“…A subclass of ELTI systems allows the extension of the technique of companding (compressing/expanding), well known in telephony and audio recording [5], to dynamical Manuscript systems; this necessitates modification of internal behavior, in such a way that the input-output behavior is preserved [4], [6], [7]. Specifically, one can compress the dynamic range of signals present at the input, process them with high noise immunity by an internally nonlinear processor, and expand the dynamic range at the output, in such a way that the input-output behavior remains linear, yet the noise transfer functions from internal points to the output are attenuated, resulting in improved output dynamic range.…”

“…Specifically, one can compress the dynamic range of signals present at the input, process them with high noise immunity by an internally nonlinear processor, and expand the dynamic range at the output, in such a way that the input-output behavior remains linear, yet the noise transfer functions from internal points to the output are attenuated, resulting in improved output dynamic range. This approach has been demonstrated for discrete-time systems based on delays [6], [7] and for conventional continuous-time systems with rational input-output transfer functions [4]. In this brief, the idea of externally linear systems, and its application to companding, is extended to CTDB systems.…”

Commutativity of first‐order discrete‐time linear time‐varying systems

“…This example covers also the validity of the results obtained for feedback systems. Although many applications of discrete time systems are considered in various digital systems, the second example is chosen from communication area and how the benefit of commutativity for reducing noise in an amplitude modulation circuit is illustrated.…”