Application of signal and noise theory to digital VLSI testing

Circuit dependent vectors like functional verification vectors, RTL test vectors, or gate-level ATPG vectors contain circuit specific information in the form of spatial correlations (among bits of a vector) and temporal correlations (among bits of the bit stream at an input pin). Some specified bits have don't care behavior because they can be changed without affecting the relevant (testing or functional) properties of the signal. In this paper, we develop a functional analysis framework for digital signals which extracts this information content from the vectors under consideration. Our proposed method is based on spectral analysis of binary bit-streams using Hadamard transform. A bit-stream corresponding to an input pin is transformed to Hadamard spectral components. The information content is distinguished from the noise in the signal using spectral analysis of random binary bit-streams. The magnitude of the spectral components represent temporal correlations while the phases of spectral components of separate bit streams represent the spatial correlations. Applications to ATPG, test compression and BIST (combinational and sequential), as described in recent publications, will benefit from this analysis, because the previous works have used ad-hoc methods for extracting spectral components from samples of test signals. We illustrate the analysis with an application to test generation for sequential benchmark circuits.