The time-varying power spectrum of a time series process quantifies the magnitude of oscillations at different frequencies and times. To obtain low-dimensional, parsimonious measures from this functional parameter, applied researchers consider collapsed measures of power within local bands of frequencies. Frequency bands commonly used in the scientific literature were historically derived, but they are not guaranteed to be optimal or justified for adequately summarizing information from a given time series. There is a dearth of methods for empirically constructing statistically optimal bands for a given signal. We seek to provide a standardized, unifying approach for deriving and analyzing customized frequency bands. A consistent, frequency-domain, iterative cumulative sum based scanning procedure is formulated to identify frequency bands that best preserve nonstationary information. A formal testing procedure is also developed to test which, if any, frequency bands remain stationary. The proposed method is used to analyze heart rate variability of a patient during sleep and uncovers a refined partition of frequency bands that best summarize the time-varying power spectrum.