TY - GEN

T1 - Sampling theorem associated with the discrete cosine transform

AU - Kovačević, Jelena

AU - Püschel, Markus

PY - 2006

Y1 - 2006

N2 - One way of deriving the discrete Fourier transform (DFT) is by equispaced sampling of periodic signals or signals on a circle. In this paper, we show that an analogous derivation can be used to obtain the DCT (type 2). To achieve this goal, we replace the circle by a line graph with symmetric boundary conditions, and define signal space, filter space, and filtering operation appropriately. Further, we derive the corresponding sampling theorem including the proper notions of "bandlimited" and "sinc function." The results show that, in a rigorous sense, the DCT is closely related to the DFT, and can be introduced without concepts from statistical signal processing as is the current practice.

AB - One way of deriving the discrete Fourier transform (DFT) is by equispaced sampling of periodic signals or signals on a circle. In this paper, we show that an analogous derivation can be used to obtain the DCT (type 2). To achieve this goal, we replace the circle by a line graph with symmetric boundary conditions, and define signal space, filter space, and filtering operation appropriately. Further, we derive the corresponding sampling theorem including the proper notions of "bandlimited" and "sinc function." The results show that, in a rigorous sense, the DCT is closely related to the DFT, and can be introduced without concepts from statistical signal processing as is the current practice.

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M3 - Conference contribution

AN - SCOPUS:33947628636

SN - 142440469X

SN - 9781424404698

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - III357-III360

BT - 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings

T2 - 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006

Y2 - 14 May 2006 through 19 May 2006

ER -