On the Uncertainty Relation for Real Signals
On the Uncertainty Relation for Real Signals
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If this condition is met, as it is in a large number of physical situations (in parti- cular, the quasi- mono chromatic optical wave trains with which Wolf is especially - 5 - concerned), than the uncertainty relation (8) can be replaced by the uncertain- ty relatica where the equality sign cannot be achieved, for the reason already mentioned o In this note, wo make two additions to the work of Gabor and Wolf, First, we develop a general inequality for the product /\t /\c d from which Wolf's re...sult follows in the special case F(0) ■ 0» In doing so, v« do not introduce the function f^(t) as an intermediate step. Second, we evaluate the uncertainty product /\t/\a> for a class of signals, whose positive frequency spectra are obtained by suppressing the negative frequencies in an arbitrary Gaussian function 1 r 2 2~1 g(ra, corres- ponding to functions of this type is always l*ss than 1/2, and becomes approxi- mately 0.
What to read after On the Uncertainty Relation for Real Signals?
You can find similar books in the "Read Also" column, or choose other free books by Irvin W Kay to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
If this condition is met, as it is in a large number of physical situations (in parti- cular, the quasi- mono chromatic optical wave trains with which Wolf is especially - 5 - concerned), than the uncertainty relation (8) can be replaced by the uncertain- ty relatica where the equality sign cannot be achieved, for the reason already mentioned o In this note, wo make two additions to the work of Gabor and Wolf, First, we develop a general inequality for the product /\t /\c d from which Wolf's re...sult follows in the special case F(0) ■ 0» In doing so, v« do not introduce the function f^(t) as an intermediate step. Second, we evaluate the uncertainty product /\t/\a> for a class of signals, whose positive frequency spectra are obtained by suppressing the negative frequencies in an arbitrary Gaussian function 1 r 2 2~1 g(ra,
What to read after On the Uncertainty Relation for Real Signals?
You can find similar books in the "Read Also" column, or choose other free books by Irvin W Kay to read onlineMoreLess
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