Identification of Systematic Absence of Cross-peaks (SACPs) in a Two-dimensional Asynchronous Spectrum using an Auxiliary 2D Quotient Spectrum and a Statistical Test

Abstract S ystematic A bsence of C ross P eaks (SACPs) in a two-dimensional (2D) asynchronous spectrum, a sensitive indicator of the signal purity, is very important in analyzing bilinear data. However, identification of SACPs in practice remains a challenge because of noise in the corresponding 2D asynchronous spectrum. We firstly show that SACP can be identified via a statistical test using a large amount of 2D asynchronous spectra. To meet the practical demand that SACPs must be identified based on a single 2D asynchronous spectrum in many cases, we use a 2D quotient spectrum (Q (x, y)) as an effective auxiliary tool to recognize SACPs. The expectation of Q(x, y) is zero when (x, y) is within SACP or background regions in the corresponding 2D asynchronous spectrum. When (x, y) is in a cross-peak region, the expectation of the absolute value of Q(x, y) is a constant regardless of whether the cross-peak in a 2D asynchronous spectrum is strong or weak. Thus, a unified threshold can be set up to differentiate the SACP region from cross-peak region via the auxiliary 2D quotient spectrum. We have applied this approach on two real-world examples and satisfactory results have been obtained. This result demonstrates that the statistical test with a 2D quotient spectrum is applicable in real-world systems.