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I have been trying to understand wavelet transformation, and many times I have come across the statement that "the wavelet transformation, unlike short-time Fourier transformation, enables us to sample higher frequencies faster, i.e. the width of the sliding window can vary".

This makes sense to me, but looking at the definition of wavelet transformation, for example this one here: Wavelet (Wolfram), I can't see what exactly enables this property. To put it simply, I can't connect the math and the explanation, and I was hoping that someone could clear this up for me.

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