Double definite integral (Fourier transform)

In summary, The conversation discusses finding a function f(x,y) by doing a backward Fourier integral to F(\omega_x, \omega_y). The speaker has two questions: if there is Fortran code for evaluating the numerical Fourier integral, and how to determine the location of simple poles in the upper half plane. The suggested resources for FFT are FFTW, GSL, and OouraFFT.
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secret2
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I don't know if this question should be posted here, but I'll give it a shot anyways.

I am trying to find f(x,y), which can be obtain by doing the backward Fourier integral to F(\omega_x, \omega_y). I have 2 questions.

1. Is there any Fortran code that could evaluate the (numerical) Fourier integral?

2. Since the function f(x,y) is 2-dimensional, we have to do a double integral. Suppose that we evaluate first the x-integral. I have a polynimial in the denominator, but the roots of the polynomial will be functions of y. Then, how can I tell if the (simple) poles are in the upper half plane or not?
 
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1. What is a double definite integral?

A double definite integral is a mathematical concept that involves finding the area under a 3-dimensional surface. It is a type of integral where both the limits of integration are definite and the function being integrated has two variables.

2. What is the Fourier transform?

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies. It converts a function from its original domain (usually time or space) to a representation in the frequency domain.

3. How is the Fourier transform related to the double definite integral?

The Fourier transform can be computed using a double definite integral. The integral represents the summation of all the different frequencies present in a signal, which is then used to create a new representation of the signal in the frequency domain.

4. What is the significance of the double definite integral in signal processing?

The double definite integral is an important tool in signal processing as it allows for the analysis and manipulation of signals in the frequency domain. This can be useful in applications such as filtering, noise reduction, and data compression.

5. Are there any real-world applications of the double definite integral and Fourier transform?

Yes, there are many real-world applications of the double definite integral and Fourier transform. They are used in fields such as engineering, physics, and mathematics for tasks such as signal processing, image processing, and data analysis.

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