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Alexander Thurdin: Osäkerhetrelationen mellan schwartzfunktioner och deras fouriertransformationer

Bachelor thesis presentation

Time: Tue 2022-06-07 10.30 - 11.30

Location: Kräftriket, house 5, room 32

Respondent: Alexander Thurdin

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For a given signal, time and frequency cannot be determined simultaneously with arbitrarily high accuracy. It’s simply not possible to determine frequencies in instantaneous time. If the time frame is too small, it will be impossible to distinguish the frequencies of the signal. On the other hand, if the frequencies are well defined, the time frame will be large. This lower limit between time and frequency will be proven in this project, the so called uncertainty principle. A central part of this project is a special type of functions, Schwartz functions, with properties that will prove useful when their fourier transform is analyzed. How this principle appears in practice will also be shown in signal processing by computers.