The difficulty he's describing also applies to wavelet transforms: higher frequency bands have wider bandwidth, so they need to be sampled more often. This mean

The difficulty he's describing also applies to wavelet transforms: higher frequency bands have wider bandwidth, so they need to be sampled more often. This means the resolution is different in different frequency bands. With the short-time fourier transform (STFT), which is widely used in Music Information Retrieval, each frequency band has the same bandwidth and is sampled at the same rate, so the output of the transform is a rectangular matrix. With a wavelet transform the output is sort of a trapezoid, because you have more samples in higher frequencies. In both cases though it's possible to losslessly round-trip the audio within numerical precision (neither the STFT nor the Wavelet transform lose information).