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> To me, it's like solution to at least 16% of all the problems I have. What are some examples of problems you've solved with Fourier series/transforms?
by sidpatil 5y ago
> To me, it's like solution to at least 16% of all the problems I have.
What are some examples of problems you've solved with Fourier series/transforms?
- melony 5y agoNot specific to Fourier but an optimized FFT implementation can be used in many places as a stand-in for convolution.
- petschge 5y agoIt's not so much a stand-in as the possibility to compute convolutions (and auto-correlation and cross-correlation) really easily and cheaply in Fourier space.
- EdvardM 5y agoThere's a good list in Wikipedia for FFT (though it's a bit more specific than just FT, but still application of it): - fast large-integer and polynomial multiplication, - efficient matrix–vector multiplication for Toeplitz,- circulant and other structured matrices, - filtering algorithms (see overlap–add and overlap–save methods), - fast algorithms for discrete cosine or sine transforms (e.g. fast DCT used for JPEG and MPEG/MP3 encoding and decoding), - fast Chebyshev approximation, - solving difference equations, - computation of isotopic distributions.[47] - modulation and demodulation of complex data symbols using orthogonal frequency division multiplexing (OFDM) for 5G, LTE, Wi-Fi, DSL, and other modern communication systems. And naturally for any time-based signal about half a gazillion applications due to it's ability to detect "traits" which can be stored/read efficiently due to time => freq transform