A Convolution Property for Sinusoidal Unitary Transforms
Summary :
This paper shows that a convolution property holds for sixteen members of a sinusoidal unitary transform family (DCTs and DSTs), on condition that an impulse response is an even function. Instead of the periodicity of an input signal assumed in the DFT case, DCTs require the input signal to be even symmetric outside boundaries and DSTs require it to be odd symmetric. The property is obtained by solving the eigenvalue problem of the matrices representing the convolution. The content of the property is that the DCT (or the DST) element of the output signal is the product of the DCT (or the DST) element of the input signal and the DFT element of the impulse response. The result for the well-known DCT is useful for a strongly-correlated signal and two examples demonstrate it.
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- IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.5 pp.856-863
- Publication Date
- 1994/05/25
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- Special Section LETTER (Special Section on Signal Processing and System Theory)
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Yasuo YOSHIDA, "A Convolution Property for Sinusoidal Unitary Transforms" in IEICE TRANSACTIONS on Fundamentals,
vol. E77-A, no. 5, pp. 856-863, May 1994, doi: .
Abstract: This paper shows that a convolution property holds for sixteen members of a sinusoidal unitary transform family (DCTs and DSTs), on condition that an impulse response is an even function. Instead of the periodicity of an input signal assumed in the DFT case, DCTs require the input signal to be even symmetric outside boundaries and DSTs require it to be odd symmetric. The property is obtained by solving the eigenvalue problem of the matrices representing the convolution. The content of the property is that the DCT (or the DST) element of the output signal is the product of the DCT (or the DST) element of the input signal and the DFT element of the impulse response. The result for the well-known DCT is useful for a strongly-correlated signal and two examples demonstrate it.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_5_856/_p
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@ARTICLE{e77-a_5_856,
author={Yasuo YOSHIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Convolution Property for Sinusoidal Unitary Transforms},
year={1994},
volume={E77-A},
number={5},
pages={856-863},
abstract={This paper shows that a convolution property holds for sixteen members of a sinusoidal unitary transform family (DCTs and DSTs), on condition that an impulse response is an even function. Instead of the periodicity of an input signal assumed in the DFT case, DCTs require the input signal to be even symmetric outside boundaries and DSTs require it to be odd symmetric. The property is obtained by solving the eigenvalue problem of the matrices representing the convolution. The content of the property is that the DCT (or the DST) element of the output signal is the product of the DCT (or the DST) element of the input signal and the DFT element of the impulse response. The result for the well-known DCT is useful for a strongly-correlated signal and two examples demonstrate it.},
keywords={},
doi={},
ISSN={},
month={May},}
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TY - JOUR
TI - A Convolution Property for Sinusoidal Unitary Transforms
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 856
EP - 863
AU - Yasuo YOSHIDA
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 1994
AB - This paper shows that a convolution property holds for sixteen members of a sinusoidal unitary transform family (DCTs and DSTs), on condition that an impulse response is an even function. Instead of the periodicity of an input signal assumed in the DFT case, DCTs require the input signal to be even symmetric outside boundaries and DSTs require it to be odd symmetric. The property is obtained by solving the eigenvalue problem of the matrices representing the convolution. The content of the property is that the DCT (or the DST) element of the output signal is the product of the DCT (or the DST) element of the input signal and the DFT element of the impulse response. The result for the well-known DCT is useful for a strongly-correlated signal and two examples demonstrate it.
ER -
English
