Heisenberg Uncertainly Principle and wavelet transform
The HUP follows directly from the properties of the Fourier Transform, because time and frequency are orthogonal bases in which we can expand the co-efficient sequence of our signal. 

In fact all pairs of orthonormal bases will have some kind of Uncertainty Principle associated with them.

In traditional Fourier analysis, the either the time axis or the frequency axis will be split into identical sized and spaced regions which permit us to gain information about the signal:


Wavelets allow you to analyse signals by splitting up the time-frequency plane into regions of different sizes. 

If you are increasing the bandwidth (i.e. frequency), you will necessarily have worse resolution in time.