Why Should we Choose between Time and Frequency?
Traditionally, transitioning from the time domain to the frequency domain involves Fourier transforms. After computations are performed in the frequency domain, inverse Fourier transform allows us to return to the time domain. However, these operations are most effective for linear behaviors and problems where phase evolution occurs slowly enough. Parseval's relation establishes a direct connection between these two domains. Leveraging Laplace's transform, which accommodates functions defined on finite domains, along with Parseval's relation applied to local time functions, enables simultaneous work in both domains. This approach facilitates solving nonlinear problems using frequency representation across various time subdomains. We provide an illustration of this technique.
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- Date: 11 Jun 2024
- Time: 02:00 PM to 03:00 PM
- All times are (UTC+02:00) Bern
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- EPFL
- Lausanne, Switzerland
- Switzerland 1015
- Building: ELG 116
- Room Number: 116
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- Co-sponsored by EMC Lab EPFL
Speakers
Dr. Olivier Maurice
Why Should we Choose between Time and Frequency?
Traditionally, transitioning from the time domain to the frequency domain involves Fourier transforms. After computations are performed in the frequency domain, inverse Fourier transform allows us to return to the time domain. However, these operations are most effective for linear behaviors and problems where phase evolution occurs slowly enough. Parseval's relation establishes a direct connection between these two domains. Leveraging Laplace's transform, which accommodates functions defined on finite domains, along with Parseval's relation applied to local time functions, enables simultaneous work in both domains. This approach facilitates solving nonlinear problems using frequency representation across various time subdomains. We provide an illustration of this technique.
Biography:
Dr. Olivier Maurice works on the tensor anlaysis of networks since 1988. Author of more than two hundred papers and five books on the subject, he has developed the concept of cords extending the formalism to complex interactions, including multiphysics as game theory. O.Maurice has a doctorate of science in electronics.
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