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Abstract
The conventional formulation of the Fourier Uncertainty Principle associated with the standard deviations methodology has several drawbacks that makes this theoretical approach often useless for practical applications. Beside of that a more practical engineering approach that discusses separately the different harmonics in any time-windows and detects signal spreading in time- and frequency domains by the relative levels, may be formulated. In contrast to the single Gaussian pulse of conventional theoretical approach, the primary model task of this engineering approach is the harmonic signal in rectangular time window. The engineering approach gives possibility to formulate the simple time-frequency uncertainty product constants, for example, 1.206709 for the 50% level detection criterion in the case of rectangular time window. Ill. 6, bibl. 15, tabl. 1 (in English; abstracts in English and Lithuanian). DOI: http://dx.doi.org/10.5755/j01.eee.117.1.1043
Highlights
The uncertainty principle or duration-bandwidth theorem is a well known fundamental result in signal analysis and in quantum mechanics, see, e.g. reviews [1, 2] and references therein
This kind of uncertainty criteria are of fundamental importance allowing to relate, e.g. uncertainty of particle momentum to the spatial spreading of wavefunction [1, 2]
In present study we will rely on the traditional complex Fourier transform s(t) S ( ) [1,2,3,4,5,6]: S
Summary
The uncertainty principle or duration-bandwidth theorem is a well known fundamental result in signal analysis and in quantum mechanics, see, e.g. reviews [1, 2] and references therein. J t ) dt but at that we will compare two different methodologies for evaluation of time-limited signals: 1) The conventional theoretical approach based on standard deviations t, of time and frequency [1, 2, 5,6,7,8] (see Appendix A) that yield the traditional inequality of the Fourier Uncertainty Principle (FUP)
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