The Discrete Fourier Transform (DFT) is a mathematical tool used to convert a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform. It is widely used in digital signal processing, image processing, and other applications such as solving partial differential equations and multiplying large integers. It can be implemented using numerical algorithms or dedicated hardware, usually employing efficient fast Fourier transform (FFT) algorithms.
UC Berkeley
Fall 2021
This course explores the role of randomness in computation and pseudorandomness, focusing on the applications in error-correcting codes, expander graphs, randomness extractors, and pseudo-random generators. The course will also address the question of derandomization of small-space computation. Prerequisites are unspecified, but the course content suggests a high level of expertise.
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