Fourier transforms are not good for analyzing nonstationary signals

I'm currently thumbing through parts of "Image Processing and Data Analysis: The Multiscale Approach." In Chapter 1, I found this enlightening comment on the Fourier transform:

The Fourier transform is well suited only to the study of stationary signals where all frequencies have an infinite coherence time, or – otherwise expressed – the signal’s statistical properties do not change over time. Fourier analysis is based on global information which is not adequate for the study of compact or local patterns.

You can find a free pdf of this book here: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.122.8536&rep=rep1&type=pdf