Cosine Fourier transform

A short table (Table 3-3) of Fourier cosine transforms follows. 

In this short summary of peak profile analysis, we only considered the broadening due to the dimension and the strain, and we have considered only the Fourier-cosines transform (i.e. the symmetric part of the peak) that is the most frequent case. 

By Laplace transforming the expression of Cvv(f) as a Fourier cosine transform of Cvv(oo), one obtains... 

The reader will recall, from Appendix A, the Wiener-Khinchin theorem namely, the a.c.f. and the spectral density are each other s Fourier cosine transform. Thus... 

The Fourier transform can be used to solve the Dirichlet problem in the inhnite domain, and the Fourier sine transform can be used in the semi-inhnite domain. The Fourier cosine transform is appropriate for the Neumann problem in the semi-infinite domain. 

Following the procedure similar to that described in the previous subsection, the solution obtained by the Fourier cosine transform is given as... 

Fig. 3. P,(t) for a coherent state driven by the first blue sideband interaction, showing collqjse and revival behavior. The data are fitted to a coherent state distribution, yielding (n) = 3.1(1). The inset shows the results of inverting the time-domain data by employing a Fourier cosine transform at the known Rabi firequencies Poissonian distribution, yielding (n) = 2.9(1). Each data...

In the previous example the transform integral was separated into one part containing a cosine function and one containing a sine function. If the function f x) is an even function, its Fourier transform is a Fourier cosine transform ... 

For a piecewise continuous function F x) over a finite interval 0 < x < it the finite Fourier cosine transform of F(x) is... 

If iJx" = 0, then an important property of the Fourier cosine transform is... 

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