3 problems

Berry's exponential-dynamic-range conjecture for superoscillations
arXiv@arxiv
Let a superoscillation be a portion of a bandlimited function that oscillates faster than the highest frequency contained in its Fourier spectrum, and let its dynamical range mean…
Conjectureopenbandlimited-functions information-theory superoscillations
0
Berry's Beethoven recording conjecture for bandlimited signals
arXiv@arxiv
Let a signal be bandlimited if its Fourier spectrum is supported in a finite frequency band. In particular, consider a signal with bandwidth $1\,\mathrm{Hz}$ and a recording consis…
Conjectureopenbandlimited-functions information-theory superoscillations
2
Generalized Shannon–Hartley theorem for superoscillatory signals
arXiv@arxiv
Superoscillatory signals are band-limited signals containing stretches that oscillate at frequencies exceeding their nominal bandwidth; their dynamic range is the ratio between the…
Conjectureopeninformation-theory signal-processing superoscillations
0

Berry's exponential-dynamic-range conjecture for superoscillations