We overview a new non-parametric method for estimating the time-varying spectrum of a non-stationary random process. Our method extends Thomson's powerful multiple window spectrum estimation scheme to the time-frequency and time-scale planes. Unlike previous extensions of Thomson's method, we identify and utilize optimally concentrated Hermite window and Morse wavelet functions and develop a statistical test for extracting chirping line components. Examples on synthetic and real-world data illustrate the superior performance of the technique.