TY - GEN
T1 - Computability of the Peak Value of Bandlimited Signals
AU - Boche, Holger
AU - Monich, Ullrich J.
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2020/5
Y1 - 2020/5
N2 - In this paper we study the peak value problem, i.e., the task of computing the peak value of a bandlimited signal from its samples. The peak value problem is important, for example, in communications, where the peak value of the transmit signal has to be controlled in order that the amplifier is not overloaded, which would generate out-of-band radiation. We prove that the peak value of a computable bandlimited signal is computable on digital hardware if oversampling is used. The computability ensures that the approximation error can be effectively controlled. Further, we provide an algorithm that can be used to perform this computation and prove that oversampling is indeed necessary, because there exist signals for which the peak value problem cannot be algorithmically solved without oversampling. Hence, without oversampling the peak value of such signals cannot be computed on any digital hardware, including DSPs, FPGAs, and CPUs.
AB - In this paper we study the peak value problem, i.e., the task of computing the peak value of a bandlimited signal from its samples. The peak value problem is important, for example, in communications, where the peak value of the transmit signal has to be controlled in order that the amplifier is not overloaded, which would generate out-of-band radiation. We prove that the peak value of a computable bandlimited signal is computable on digital hardware if oversampling is used. The computability ensures that the approximation error can be effectively controlled. Further, we provide an algorithm that can be used to perform this computation and prove that oversampling is indeed necessary, because there exist signals for which the peak value problem cannot be algorithmically solved without oversampling. Hence, without oversampling the peak value of such signals cannot be computed on any digital hardware, including DSPs, FPGAs, and CPUs.
KW - Peak value
KW - algorithm
KW - bandlimited signal
KW - computability
KW - oversampling
UR - http://www.scopus.com/inward/record.url?scp=85089218017&partnerID=8YFLogxK
U2 - 10.1109/ICASSP40776.2020.9053211
DO - 10.1109/ICASSP40776.2020.9053211
M3 - Conference contribution
AN - SCOPUS:85089218017
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 5280
EP - 5284
BT - 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020
Y2 - 4 May 2020 through 8 May 2020
ER -