-dimensional Fourier Transform

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Chapter 8. n -dimensional Fourier Transform Space, the Final Frontier To quote Ron Bracewell from p. 119 of his book Two -dimensional Imaging, In two dimensions phenomena are richer than in one dimension. True enough, working in two dimensions offers many new and rich possibilities. Contemporary applications of the Fourier Transform are just as likely to come from problems in two, three, and even higher dimensions as they are in one imaging is one obvious and important example. To capitalize on the work we've already done, however, as well as to highlight differences between the one- dimensional case and higher dimensions, we want to mimic the one -dimensional setting and arguments as much as possible.

It’s still the case that the complex conjugate of the integral is the integral of the complex conjugate, so when f(x) is real valued, Ff(−ξ) = Ff(ξ). Finally, evenness and oddness are defined exactly as in the one-dimensional case. That is: f(x) is even if f(−x) = f(x), or without writing the variables, if f− = f.

  Variable, Complex, Transform, Fourier, Fourier transform