It is said that you leave Oxford with either
Subdepartment of the Department of Physics of the University of Oxford by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16Group of students that represent students academic views about the courses.
Symmetry in Condensed Matter Physics course of the University of Oxford by Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16www2.physics.ox.ac.uk/students/course-materials/symmetry-in-condensed-matter-physics# Archive: web.archive.org/web/20230804204137/https://www2.physics.ox.ac.uk/students/course-materials/symmetry-in-condensed-matter-physics Lecture notes from 2019.
Professor: Radu Coldea
Atomic and laser Physics subdepartment of the University of Oxford by Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16
Published as: arxiv.org/pdf/2304.03442.pdf Generative Agents: Interactive Simulacra of Human Behavior by Park et al.
AI Agents Behaving Like Humans by Prompt Engineering (2023)
Source. See sections: "Example 1 - N even", "Example 2 - N odd" and "Representation in terms of sines and cosines" of www.statlect.com/matrix-algebra/discrete-Fourier-transform-of-a-real-signal
The transform still has complex numbers.
Summary:Therefore, we only need about half of to represent the signal, as the other half can be derived by conjugation.
- is real
"Representation in terms of sines and cosines" from www.statlect.com/matrix-algebra/discrete-Fourier-transform-of-a-real-signal then gives explicit formulas in terms of .
NumPy for example has "Real FFTs" for this: numpy.org/doc/1.24/reference/routines.fft.html#real-ffts
DFT of with 25 points
. Source at: numpy/fft_plot.py. This plot illustrates how the DFT of a real signal is symmetric around the middle point, and so only half of the transform points are needed to reconstruct the original signal. We also see how the phase of the sinusoids determines if their DFT components are real or imaginary.An efficient algorithm to calculate the discrete Fourier transform.
Leo Szilard: The Genius Behind the Bomb
. Source. 1992. TODO an external link to the production? Producers credited at end: Helen Weiss and Alain Jehlen. As indicated at: archive.org/details/TheGeniusBehindtheBomb it was apparently produced by WGBH, public radio station from Boston. There are unlisted articles, also show them or only show them.