The bias-variance trade-off is an important issue is spectrum estimation. In 1982, Thomson introduced a powerful multiple window method for stationary signals that deals with the bias-variance trade-off in an optimal fashion. In this thesis, we extend Thomson's method to the time-frequency and time-scale planes, and propose a new method to estimate the time-varying spectrum of non-stationary random processes. Unlike previous extensions of Thomson's method, we identify and utilize optimally concentrated window and wavelet functions, and develop a statistical test for detecting chirping line components. The optimal windows are the Hermite functions for time-frequency analysis, and the Morse wavelets for time-scale analysis.