SCOAP is a program developed at Sandia National Laboratories for the analysis of digital circuit testability. Testability is related to the difficulty of controlling and observing the logical values of internal nodes from circuit inputs and outputs, respectively. This paper reviews the testability analysis algorithms and describes their implementation in the SCOAP program.

The system considered here consists of a differential pulse-code modulator (DPCM) in which the quantizer is replaced by an adaptive quantizer. Adaptation is accomplished by adjusting the stepsize at every sampling instant, depending upon the magnitude of the quantization error. Quantizing noise in adaptive DPCM (ADPCM) systems falls into three categories: granularity, slope overload, and quantizer saturation. Granular noise occurs because only a finite number of levels are available to represent the analog input signal during the encoding process. Slope overload happens when the slope of the input signal increases faster than the adaptive system can follow. Quantizer saturation exists because nonoptimal decisions on step-size adjustments can lead to situations in which quantizer overload occurs without slope overload. The result is an error larger than a purely granular noise analysis would suggest. Equations for the three types of quantizing noise in ADPCM systems are derived, and computer simulations are perforated. For flatand RC-filtered Gaussian input signals, oversampled at various rates, the simulation results agree well with theoretical predictions. Comparisons indicate that the ADPCM can perform better than the best analogous nonadaptive system in terms of signal-to-quantizing-noise ratio. Furthermore, the optimal operating point for the ADPCM is much less sensitive to changes in input signal parameters and system component values than in nonadaptive systems.

An adaptive differential pulse code modulator (ADPCM) with a finite number of possible step-sizes and a leaky integrator in the feedback loop is considered. A zero-mean unit-ariance first-order Markov sequence is chosen as the input to thc system, and the leak parameter of the ADPCM accumulator is made equal to the intersample correlation of the input sequence. Using this fundamental structure, a method is presented for computing the exact joint probability distribution function of quantization error and step-size in ADPCM. From the joint distribution, marginal quantization error, and step-size distributions are obtained for Gauss-Markov, exponential-Markov, and uniform-Markov input signals. Empirical distributions obtained from simulations agree very well with their theoretical counterparts.

The problem of stability of an adaptive differential pulse code modulation (ADPCM) system is considered from two viewpoints. First, it is demonstrated that the step-size adaptation algorithm of a certain class of ADPCM's can be characterized by the system's response to step: function inputs. The degree of "hunting" or "oscillation" provides an indication of the deterministic stability of the algorithm, and algorithms are presented that minimize these effects. Secondly, stationary random processes with rational spectral densities are used to study stochastic stability of ADPCM. It is shown that for certain ADPCM's the time-averaged mean-absolute quantizing noise is bounded, that the joint distribution of the input and decoded output processes possesses a stationary distribution, that this joint distribution converges to the stationary distribution from an arbitrary starting point, and that the mean-absolute quantizing noise is finite under the stationary distribution.