# Heisenberg Uncertainly Principle and wavelet transform

I am using CMOR(complex morlet) wavelet in Fourier space in order to reconstruct my signal and also estimate damping and frequencies of the embedded modes. there are two main parameters in cmor. the Fb and Fc. bandwidth and center frequency, with increasing the Fb i get better result for frequency estimation, but i cant get a good damping estimation with high Fb. is it sth to do with Heisenberg Uncertainly Principle? and if yes, would you explain the role of fb and fc in the accuracy of frequency and damping estimations? The wavelet transforms provide a unified framework for getting around the Heisenberg Uncertainly Principle.

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.