where and are the standard deviations of the time and frequency energy concentrations respectively. The minimum is attained for a Gaussian-shaped pulse (Gabor wavelet) [For the un-squared Gaussian (i.e. signal amplitude) and its un-squared Fourier transform magnitude ; squaring reduces each by a factor .] Another common measure is the product of the time and frequency full width at half maximum (of the power/energy), which for the Gaussian equals (see bandwidth-limited pulse).
where .and are the standard deviations of the time and frequency energy concentrations respectively The minimum is attained for a Gaussian-shaped pulse (Gabor wavelet) [For the un-squared Gaussian (i.e. signal amplitude) and its un-squared Fourier transform magnitude ; squaring reduce.s each by a factor .] Another common measure is the product of the time and frequency full width at half maximum (of the power/energy), which for the Gaussian equals (see bandwidth-limited pulse)