Application of Signal and Noise Theory to Digital VLSI Testing ∗

Abstract – We analyze input signals of digital circuits. Typical signals are functional inputs, test vectors, or simply random inputs. Bits in a sequence of vectors contain spatial correlation (among bits of a vector) and temporal correlation (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. A given sequence of vectors that can be functional verification vectors, RTL test vectors, or gate-level ATPG vectors for a fault sample, is analyzed. A bit stream of n bits corresponding to an input pin is considered a sample signal to be analyzed. The bit stream is resolved in terms of n Hadamard functions, which form a complete basis set for any stream of n bits. The total power of this spectrum is normalized to unity and all Hadamard components with power below a threshold 2/n are regarded as noise. This threshold represents twice the component power level of the ideal spectrum of a random bit stream, which contains all n Hadamard components in equal magnitude (analogous to white noise). The spectral components of a bit stream represent temporal correlation while the phases of spectral components of separate bit streams represent the spatial correlation. Applications to ATPG, test compression and BIST (combinational and sequential), as described in recent publications will benefit from this analysis. This is because the previous works have used ad-hoc methods for extracting spectral components from samples of test signals. We illustrate the analysis with applications to sequential benchmark circuits. 1