The Fourier Transform is a very useful and ingenious thing. But how was it initiated? How did Joseph Fourier composed the Fourier Transform formula and the idea of a transformation …

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Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …

Mar 12, 2020 · Why are the limits of the fourier cosine/sine series [0,∞) while the limits of the fourier exponential series are (-∞,∞)? 3 How does this definition of Fourier transform in Fulton …

There's a family of functions that differ by additive constants and all have the same derivative. Their Fourier transforms differ by deltas at the origin (proportional to the additive constants), …

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …

The Fourier transform is a different representation that makes convolutions easy. Or, to quote directly from there: "the Fourier transform is a unitary change of basis for functions (or …

May 12, 2020 · The FT of even functions are also even; The FT of odd functions are also odd. The real part of the FT of a real function is even; The imaginary part of the FT of a real …

Jan 5, 2025 · $\begingroup$ @Rodri Ah, I see you have got it backward: in order to find differential equations in Fourier space, we do not take the Fourier transform of the equation, …

Let us consider the Fourier transform of $\mathrm{sinc}$ function. As I know it is equal to a rectangular function in frequency domain and I want to get it myself, I know there is a lot of …