| We present techniques for modifying the internal signals in a given linear time invariant (LTI) digital signal processor (DSP) prototype, without causing any output disturbances. The resulting system is referred to as an externally LTI (ELTI) system. Although the ELTI system is in general internally time-varying and/or internally nonlinear, the external input-output behavior is LTI and identical to that of the prototype LTI system. We present two general techniques for obtaining ELTI systems from an LTI prototype. In the first technique, internal modification is accomplished using dynamic-scaling signals, while in the second technique, internal modification is accomplished using memoryless, invertible nonlinear functions.;Hardware implementations of the companding DSPs are presented, corresponding to several LTI prototype systems. In the syllabic companding DSP technique, compression is achieved using dynamic-scaling signals based on the envelopes of signals in the prototype DSP. An analog front-end circuit, designed and prototyped on a printed circuit board, provides the compressed input and corresponding dynamic-scaling signal, based on the input envelope; the envelope detection is performed digitally. In the instantaneous companding DSP technique, compression is achieved using a memoryless, invertible, compressive nonlinear function; the choice of nonlinear function is discussed, and an efficient hardware implementation for the "classical" standard 15-segment piecewise-linear approximation to the 255-mu law is developed. The digital portions of all systems have been implemented on an FPGA, using only simple, low-resolution fixed-point arithmetic.;Measurements of the SNRs at the output of our hardware implementations verify the presented theoretical results. When the implementations are tested with complex audio material, the noise at the output of the companding systems is significantly lower, and far less audible, than the noise at the output of a conventional fixed-point system of the same resolution, and for the companding systems, the noise is noticeably reduced, and essentially inaudible, during quieter segments of the audio.;The presented companding techniques are also applied to efficiently process MPEG-encoded signals during the decoding process, using only efficient fixed-point arithmetic operations. Due to the companding techniques, a large SNR is achieved over a wide range of input levels, so that there is only significant quantization noise in subbands that simultaneously contain a "large" signal. Thus, due to psychoacoustic masking effects, the perceived audible quantization noise at the output of the system is relatively low, even though only low-resolution fixed-point operations are used in the processing.;In this work, the presented ELTI techniques are applied to compress the dynamic range (DR) of the input, output, and all internal states of a fixed-point DSP, such that they always stay close to full-scale, thus spanning most of the available bits and making possible a large signal-to-quantization-noise-ratio (SNR) over a large input range. We show that such application of the ELTI techniques is an extension of companding (compressing/expanding) to DSPs. In this work, both syllabic and instantaneous companding are extended to DSPs; an equation is derived for predicting the SNR at the output of a syllabic companding DSP. |
