Spectral Domain Noise Modeling in Compressive Sensing-Based Tonal Signal Detection

Chenlin HU; Jin Young KIM; Seung Ho CHOI; Chang Joo KIM

doi:10.1587/transfun.E98.A.1122

Spectral Domain Noise Modeling in Compressive Sensing-Based Tonal Signal Detection

Chenlin HU, Jin Young KIM, Seung Ho CHOI, Chang Joo KIM

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Tonal signals are shown as spectral peaks in the frequency domain. When the number of spectral peaks is small and the spectral signal is sparse, Compressive Sensing (CS) can be adopted to locate the peaks with a low-cost sensing system. In the CS scheme, a time domain signal is modelled as $oldsymbol{y}=Phi F^{-1}oldsymbol{s}$, where y and s are signal vectors in the time and frequency domains. In addition, F^-1 and $Phi$ are an inverse DFT matrix and a random-sampling matrix, respectively. For a given y and $Phi$, the CS method attempts to estimate s with l₀ or l₁ optimization. To generate the peak candidates, we adopt the frequency-domain information of $ esmile{oldsymbol{s}}$ = $oldsymbol{F} esmile{oldsymbol{y}}$, where $ esmile{y}$ is the extended version of y and $ esmile{oldsymbol{y}}left(oldsymbol{n} ight)$ is zero when n is not elements of CS time instances. In this paper, we develop Gaussian statistics of $ esmile{oldsymbol{s}}$. That is, the variance and the mean values of $ esmile{oldsymbol{s}}left(oldsymbol{k} ight)$ are examined.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.5 pp.1122-1125

Publication Date: 2015/05/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E98.A.1122

Type of Manuscript: LETTER

Category: Digital Signal Processing

Authors

Chenlin HU
  Chonnam National University
Jin Young KIM
  Chonnam National University
Seung Ho CHOI
  Dongshin University
Chang Joo KIM
  ETRI

Keyword

compressive sensing, tonal signal detection, noise modeling

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Chenlin HU, Jin Young KIM, Seung Ho CHOI, Chang Joo KIM, "Spectral Domain Noise Modeling in Compressive Sensing-Based Tonal Signal Detection" in IEICE TRANSACTIONS on Fundamentals, vol. E98-A, no. 5, pp. 1122-1125, May 2015, doi: 10.1587/transfun.E98.A.1122.
Abstract: Tonal signals are shown as spectral peaks in the frequency domain. When the number of spectral peaks is small and the spectral signal is sparse, Compressive Sensing (CS) can be adopted to locate the peaks with a low-cost sensing system. In the CS scheme, a time domain signal is modelled as $oldsymbol{y}=Phi F^{-1}oldsymbol{s}$, where y and s are signal vectors in the time and frequency domains. In addition, F^-1 and $Phi$ are an inverse DFT matrix and a random-sampling matrix, respectively. For a given y and $Phi$, the CS method attempts to estimate s with l₀ or l₁ optimization. To generate the peak candidates, we adopt the frequency-domain information of $ esmile{oldsymbol{s}}$ = $oldsymbol{F} esmile{oldsymbol{y}}$, where $ esmile{y}$ is the extended version of y and $ esmile{oldsymbol{y}}left(oldsymbol{n} ight)$ is zero when n is not elements of CS time instances. In this paper, we develop Gaussian statistics of $ esmile{oldsymbol{s}}$. That is, the variance and the mean values of $ esmile{oldsymbol{s}}left(oldsymbol{k} ight)$ are examined.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.1122/_p

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@ARTICLE{e98-a_5_1122,
author={Chenlin HU, Jin Young KIM, Seung Ho CHOI, Chang Joo KIM, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Spectral Domain Noise Modeling in Compressive Sensing-Based Tonal Signal Detection},
year={2015},
volume={E98-A},
number={5},
pages={1122-1125},
abstract={Tonal signals are shown as spectral peaks in the frequency domain. When the number of spectral peaks is small and the spectral signal is sparse, Compressive Sensing (CS) can be adopted to locate the peaks with a low-cost sensing system. In the CS scheme, a time domain signal is modelled as $oldsymbol{y}=Phi F^{-1}oldsymbol{s}$, where y and s are signal vectors in the time and frequency domains. In addition, F^-1 and $Phi$ are an inverse DFT matrix and a random-sampling matrix, respectively. For a given y and $Phi$, the CS method attempts to estimate s with l₀ or l₁ optimization. To generate the peak candidates, we adopt the frequency-domain information of $ esmile{oldsymbol{s}}$ = $oldsymbol{F} esmile{oldsymbol{y}}$, where $ esmile{y}$ is the extended version of y and $ esmile{oldsymbol{y}}left(oldsymbol{n} ight)$ is zero when n is not elements of CS time instances. In this paper, we develop Gaussian statistics of $ esmile{oldsymbol{s}}$. That is, the variance and the mean values of $ esmile{oldsymbol{s}}left(oldsymbol{k} ight)$ are examined.},
keywords={},
doi={10.1587/transfun.E98.A.1122},
ISSN={1745-1337},
month={May},}

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TY - JOUR
TI - Spectral Domain Noise Modeling in Compressive Sensing-Based Tonal Signal Detection
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1122
EP - 1125
AU - Chenlin HU
AU - Jin Young KIM
AU - Seung Ho CHOI
AU - Chang Joo KIM
PY - 2015
DO - 10.1587/transfun.E98.A.1122
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2015
AB - Tonal signals are shown as spectral peaks in the frequency domain. When the number of spectral peaks is small and the spectral signal is sparse, Compressive Sensing (CS) can be adopted to locate the peaks with a low-cost sensing system. In the CS scheme, a time domain signal is modelled as $oldsymbol{y}=Phi F^{-1}oldsymbol{s}$, where y and s are signal vectors in the time and frequency domains. In addition, F^-1 and $Phi$ are an inverse DFT matrix and a random-sampling matrix, respectively. For a given y and $Phi$, the CS method attempts to estimate s with l₀ or l₁ optimization. To generate the peak candidates, we adopt the frequency-domain information of $ esmile{oldsymbol{s}}$ = $oldsymbol{F} esmile{oldsymbol{y}}$, where $ esmile{y}$ is the extended version of y and $ esmile{oldsymbol{y}}left(oldsymbol{n} ight)$ is zero when n is not elements of CS time instances. In this paper, we develop Gaussian statistics of $ esmile{oldsymbol{s}}$. That is, the variance and the mean values of $ esmile{oldsymbol{s}}left(oldsymbol{k} ight)$ are examined.
ER -