A Computing Method for Linear Convolution and Linear Correlation in the DCT Domain
Summary :
We propose a computing method for linear convolution and linear correlation between sequences using discrete cosine transform (DCT). Zero-padding is considered as well as linear convolution using discrete Fourier transform (DFT). Analyzing the circular convolution between symmetrically extended sequences, we derive the condition for zero-padding before and after the sequences. The proposed method can calculate linear convolution for any filter and also calculate linear correlation without reversing one of the input sequences. The computational complexity of the proposed method is lower than that of linear convolution using DFT.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E96-A No.7 pp.1518-1525
- Publication Date
- 2013/07/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E96.A.1518
- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
Authors
Izumi ITO
Tokyo Institute of Technology
Keyword
Latest Issue
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Izumi ITO , "A Computing Method for Linear Convolution and Linear Correlation in the DCT Domain" in IEICE TRANSACTIONS on Fundamentals,
vol. E96-A, no. 7, pp. 1518-1525, July 2013, doi: 10.1587/transfun.E96.A.1518.
Abstract: We propose a computing method for linear convolution and linear correlation between sequences using discrete cosine transform (DCT). Zero-padding is considered as well as linear convolution using discrete Fourier transform (DFT). Analyzing the circular convolution between symmetrically extended sequences, we derive the condition for zero-padding before and after the sequences. The proposed method can calculate linear convolution for any filter and also calculate linear correlation without reversing one of the input sequences. The computational complexity of the proposed method is lower than that of linear convolution using DFT.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E96.A.1518/_p
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@ARTICLE{e96-a_7_1518,
author={Izumi ITO , },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Computing Method for Linear Convolution and Linear Correlation in the DCT Domain},
year={2013},
volume={E96-A},
number={7},
pages={1518-1525},
abstract={We propose a computing method for linear convolution and linear correlation between sequences using discrete cosine transform (DCT). Zero-padding is considered as well as linear convolution using discrete Fourier transform (DFT). Analyzing the circular convolution between symmetrically extended sequences, we derive the condition for zero-padding before and after the sequences. The proposed method can calculate linear convolution for any filter and also calculate linear correlation without reversing one of the input sequences. The computational complexity of the proposed method is lower than that of linear convolution using DFT.},
keywords={},
doi={10.1587/transfun.E96.A.1518},
ISSN={1745-1337},
month={July},}
Copy
TY - JOUR
TI - A Computing Method for Linear Convolution and Linear Correlation in the DCT Domain
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1518
EP - 1525
AU - Izumi ITO
PY - 2013
DO - 10.1587/transfun.E96.A.1518
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E96-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2013
AB - We propose a computing method for linear convolution and linear correlation between sequences using discrete cosine transform (DCT). Zero-padding is considered as well as linear convolution using discrete Fourier transform (DFT). Analyzing the circular convolution between symmetrically extended sequences, we derive the condition for zero-padding before and after the sequences. The proposed method can calculate linear convolution for any filter and also calculate linear correlation without reversing one of the input sequences. The computational complexity of the proposed method is lower than that of linear convolution using DFT.
ER -
English
