TY - GEN
T1 - Analytic Properties of Downsampling for Bandlimited Signals
AU - Boche, Holger
AU - Monich, Ullrich J.
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/5
Y1 - 2019/5
N2 - In this paper we study downsampling for bandlimited signals. Downsampling in the discrete-time domain corresponds to a removal of samples. For any downsampled signal that was created from a bandlimited signal with finite energy, we can always compute a bandlimited continuous-time signal such that the samples of this signal, taken at Nyquist rate, are equal to the downsampled discrete-time signal. However, as we show, this is no longer true for the space of bounded bandlimited signals that vanish at infinity. We explicitly construct a signal in this space, which after downsampling does not have a bounded bandlimited interpolation. This shows that downsampling in this signal space is an operation that can lead out of the set of discrete-time signals for which we have a one-to-one correspondence with continuous-time signals.
AB - In this paper we study downsampling for bandlimited signals. Downsampling in the discrete-time domain corresponds to a removal of samples. For any downsampled signal that was created from a bandlimited signal with finite energy, we can always compute a bandlimited continuous-time signal such that the samples of this signal, taken at Nyquist rate, are equal to the downsampled discrete-time signal. However, as we show, this is no longer true for the space of bounded bandlimited signals that vanish at infinity. We explicitly construct a signal in this space, which after downsampling does not have a bounded bandlimited interpolation. This shows that downsampling in this signal space is an operation that can lead out of the set of discrete-time signals for which we have a one-to-one correspondence with continuous-time signals.
KW - bandlimited interpolation
KW - bandlimited signal
KW - boundedness
KW - downsampling
UR - http://www.scopus.com/inward/record.url?scp=85064643679&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2019.8683894
DO - 10.1109/ICASSP.2019.8683894
M3 - Conference contribution
AN - SCOPUS:85064643679
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 5008
EP - 5012
BT - 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
Y2 - 12 May 2019 through 17 May 2019
ER -