The current document is directed to methods and systems for frequency-domain analysis of operational and performance metric values and other data generated and collected within computer systems, including large distributed computer systems and virtualized data centers. In one implementation, each set of time-ordered values for each metric in a set of metrics is partitioned into time intervals, transformed from the time domain to the frequency domain, and aligned to generate a metric surface in a frequency-time-amplitude space. The metric surfaces are then pairwise compared to identify related metrics. Transfer functions are generated for transforming metric surfaces into one another. The comparison values and transfer functions are used to produce graphs that encapsulate discovered relationships between metrics.