A method is provided for performing real-time spectral analysis of a non-stationary signal. The method includes sampling the non-stationary signal, using an observation window having a length short enough to approximate a stationary signal, to provide an initial set of sampled data, buffering the initial set of sampled data to obtain multiple buffered sets of sampled data, filtering the initial set of sampled data and the buffered sets of sampled data, using corresponding filter responses, to obtain multiple filtered sets of sampled data, and performing a chirp-z-transform (CZT) of the filtered sets of sampled data to provide a set of discrete Fourier transforms (DFT) coefficients. A total signal spectrum of the non-stationary signal is reconstructed using the set of DFT coefficients.