TY - GEN
T1 - Optimal Sampling Rate and Bandwidth of Bandlimited Signals-An Algorithmic Perspective
AU - Boche, Holger
AU - Monich, Ullrich J.
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2020/5
Y1 - 2020/5
N2 - The bandwidth of a bandlimited signal is a key quantity that is relevant in numerous applications. For example, it determines the minimum sampling rate that is necessary to reconstruct a bandlimited signal from its samples. In this paper we study if it is possible to algorithmically determine the actual bandwidth of a bandlimited signal. We prove that this is not possible in general, because there exist bandlimited computable signals, which have a bandwidth that is not computable. To this end we employ the concept of Turing computability, which provides a theoretical model that describes the fundamental limits of any practically realizable digital hardware, such as CPUs, DSPs, or FPGAs. Further, we answer the weaker question if it can be algorithmically answered whether the bandwidth of a given signal is larger than a predefined value.
AB - The bandwidth of a bandlimited signal is a key quantity that is relevant in numerous applications. For example, it determines the minimum sampling rate that is necessary to reconstruct a bandlimited signal from its samples. In this paper we study if it is possible to algorithmically determine the actual bandwidth of a bandlimited signal. We prove that this is not possible in general, because there exist bandlimited computable signals, which have a bandwidth that is not computable. To this end we employ the concept of Turing computability, which provides a theoretical model that describes the fundamental limits of any practically realizable digital hardware, such as CPUs, DSPs, or FPGAs. Further, we answer the weaker question if it can be algorithmically answered whether the bandwidth of a given signal is larger than a predefined value.
KW - Bandwidth
KW - algorithm
KW - bandlimited signal
KW - computability
UR - http://www.scopus.com/inward/record.url?scp=85089220194&partnerID=8YFLogxK
U2 - 10.1109/ICASSP40776.2020.9053158
DO - 10.1109/ICASSP40776.2020.9053158
M3 - Conference contribution
AN - SCOPUS:85089220194
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 5905
EP - 5909
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 -