In practice, radio astronomers rarely recover the brightness distribution of a source by directly taking the inverse Fourier transform of a measured visibility function.
22.
In many situations the basic strategy is to apply the Fourier transform, perform some operation or simplification, and then apply the inverse Fourier transform.
23.
For this reason the properties of the Fourier transform hold for the inverse Fourier transform, such as the Convolution theorem and the Riemann Lebesgue lemma.
24.
The infinitesimal term in the denominator is a small positive number which guarantees that the inverse Fourier transform in will be nonzero only for future times.
25.
These surveys required intensive use of inverse Fourier Transforms, and were made possible by development of a new generation of computers such as the Titan.
26.
The drawback is that it's computationally inefficient due to the requirement of 2-D inverse Fourier transform and hence less useful in practice.
27.
The inverse Fourier transform is extremely similar to the original Fourier transform : as discussed above, it differs only in the application of a flip operator.
28.
This results in an ill-posed inverse problem as any phase could be assigned to the amplitudes prior to an inverse Fourier transform to real space.
29.
This second sum is a Riemann sum, and so by letting it will converge to the integral for the inverse Fourier transform given in the definition section.
30.
In this case the integral in the inverse Fourier transform is defined with the aid of a smooth rather than a sharp cut off function; specifically we define
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