Reconstruction of Signal and Its Fourier Spectra from Irregularly Distributed Samples
Summary :
We introduce a procedure to determine the discrete Fourier spectra of the band-limited function from its irregularly distributed samples. The nonuniform data of the signal are represented by the non-orthogonal basis functions (non-harmonic Fourier functions) and discrete Fourier spectra of the signal. We construct a set of orthonormal basis functions from the above mentioned non-orthogonal basis functions using the Gram-Schmidt procedure. Based on the G-S procedure and the property of the orthogonalization, the spectral components of signal can be obtained by the conjugate transpose of orthonormal basis functions, their coefficients matrix and the nonuniform samples. Thus the desired signal can be obtained by the inverse Fourier transform of the determined discrete Fourier spectra. We apply this algorithm to reconstruct a band-limited low-pass and band-pass signal and show that our method provide more stable and better reconstruction than the matrix inversion method.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.10 pp.1714-1717
- Publication Date
- 1994/10/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- LETTER
- Category
- Digital Signal Processing
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Yongwan PARK, "Reconstruction of Signal and Its Fourier Spectra from Irregularly Distributed Samples" in IEICE TRANSACTIONS on Fundamentals,
vol. E77-A, no. 10, pp. 1714-1717, October 1994, doi: .
Abstract: We introduce a procedure to determine the discrete Fourier spectra of the band-limited function from its irregularly distributed samples. The nonuniform data of the signal are represented by the non-orthogonal basis functions (non-harmonic Fourier functions) and discrete Fourier spectra of the signal. We construct a set of orthonormal basis functions from the above mentioned non-orthogonal basis functions using the Gram-Schmidt procedure. Based on the G-S procedure and the property of the orthogonalization, the spectral components of signal can be obtained by the conjugate transpose of orthonormal basis functions, their coefficients matrix and the nonuniform samples. Thus the desired signal can be obtained by the inverse Fourier transform of the determined discrete Fourier spectra. We apply this algorithm to reconstruct a band-limited low-pass and band-pass signal and show that our method provide more stable and better reconstruction than the matrix inversion method.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_10_1714/_p
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@ARTICLE{e77-a_10_1714,
author={Yongwan PARK, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Reconstruction of Signal and Its Fourier Spectra from Irregularly Distributed Samples},
year={1994},
volume={E77-A},
number={10},
pages={1714-1717},
abstract={We introduce a procedure to determine the discrete Fourier spectra of the band-limited function from its irregularly distributed samples. The nonuniform data of the signal are represented by the non-orthogonal basis functions (non-harmonic Fourier functions) and discrete Fourier spectra of the signal. We construct a set of orthonormal basis functions from the above mentioned non-orthogonal basis functions using the Gram-Schmidt procedure. Based on the G-S procedure and the property of the orthogonalization, the spectral components of signal can be obtained by the conjugate transpose of orthonormal basis functions, their coefficients matrix and the nonuniform samples. Thus the desired signal can be obtained by the inverse Fourier transform of the determined discrete Fourier spectra. We apply this algorithm to reconstruct a band-limited low-pass and band-pass signal and show that our method provide more stable and better reconstruction than the matrix inversion method.},
keywords={},
doi={},
ISSN={},
month={October},}
Copy
TY - JOUR
TI - Reconstruction of Signal and Its Fourier Spectra from Irregularly Distributed Samples
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1714
EP - 1717
AU - Yongwan PARK
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 1994
AB - We introduce a procedure to determine the discrete Fourier spectra of the band-limited function from its irregularly distributed samples. The nonuniform data of the signal are represented by the non-orthogonal basis functions (non-harmonic Fourier functions) and discrete Fourier spectra of the signal. We construct a set of orthonormal basis functions from the above mentioned non-orthogonal basis functions using the Gram-Schmidt procedure. Based on the G-S procedure and the property of the orthogonalization, the spectral components of signal can be obtained by the conjugate transpose of orthonormal basis functions, their coefficients matrix and the nonuniform samples. Thus the desired signal can be obtained by the inverse Fourier transform of the determined discrete Fourier spectra. We apply this algorithm to reconstruct a band-limited low-pass and band-pass signal and show that our method provide more stable and better reconstruction than the matrix inversion method.
ER -
English
