Microtubules are linear polymers of the cytoskeleton that serve to organize the cytoplasm of eukaryotic cells. Understanding how microtubule polymers self-assemble is important in biotechnology including the development of novel cancer therapies and proper guidance of regenerating neurons. The assembly of microtubules occurs by a unique process whereby an individual microtubule undergoes abrupt and apparently, stochastic switching between alternating steady states of growth and shrinkage, a phenomenon known as microtubule dynamic instability. To characterize these oscillations spectral (frequency-domain) analysis, commonly used in engineering for system identification, was applied. Power spectra of the individual microtubule-length life histories revealed oscillations within growth phases, directly reflecting acceleration and deceleration in the growth process. These fluctuations were not accounted for by the standard two-state model commonly used in the analysis of microtubule assembly, despite the inclusion of simulated measurement error in the model. Thus the spectral analysis of microtubule assembly permitted characterization of assembly process dynamics independent of particular assembly models, and as such represents a powerful analytical framework within which to study microtubule dynamic instability and assess its function in vivo.