The eigenvalues of matrices that occur in certain interpolation problems

Ferreira, Paulo J. S. G.

doi:10.1109/78.611226

Cited by 20 publications

(11 citation statements)

References 20 publications

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“…Note that the eigenvalues of matrices like H H * where studied in detail in [17]. These results indicate that every universal sampling pattern shows a similar poor behavior.…”

Section: A Robustness Of the Sampling Schemementioning

confidence: 82%

“…Thus, also with respect to the noise enhancement of Γ it is very beneficial to adapt the sampling pattern to the band location pattern such that the condition number / becomes as low as possible. Note that (17) gives only bounds on the noise enhancement. The actual value of 2 out is given by (16).…”

Section: ∈ℤmentioning

confidence: 99%

“…We apply a multicoset sampling scheme with = 3 sampling filters and we compare the universal sampling pattern 0 with the optimized sampling pattern which minimizes the condition number / for every band location. For each 3 , the lower and upper bound of the noise enhancement 2 out / 2 is computed using (17). The factor was introduced for normalization, taking into account that we only extract 1 out of signal streams.…”

Section: Examplementioning

confidence: 99%

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A cognitive radio architecture based on sub-Nyquist sampling

Wieruch

Pohl

2011

2011 IEEE International Symposium on Dynamic Spectrum Access Networks (DySPAN)

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In this paper we discuss a cognitive radio architecture based on sub-Nyquist sampling scheme. At present, analog-to-digital converters can process wide-band signals up to 1GHz and therefore convert it into the digital baseband. To deal with the limited processing power a multicoset sampling filter in the digital domain is introduced. Thus, it is possible to have a fully flexible multiband filter for a wide-band signal with up to 1GHz bandwidth. In particular, the multiband receiver can deal with a flexible set of sub-bands with fair digital signal processing power and fast adaption

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“…Note that the eigenvalues of matrices like H H * where studied in detail in [17]. These results indicate that every universal sampling pattern shows a similar poor behavior.…”

Section: A Robustness Of the Sampling Schemementioning

confidence: 82%

Section: ∈ℤmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

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A cognitive radio architecture based on sub-Nyquist sampling

Wieruch

Pohl

2011

2011 IEEE International Symposium on Dynamic Spectrum Access Networks (DySPAN)

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“…References [3]- [8] have studied the effects of the different patterns of errors (different values of k l ) on the stability of the DFT codes. They have proved that the DFT codes are vulnerable to the burst of errors which is the consecutive form of k l .…”

Section: Dft Codesmentioning

confidence: 99%

Introducing stable oversampling patterns for DFT error recovery codes in bursty erasure channels

Momenai

Talebi

2007

2007 9th International Symposium on Signal Processing and Its Applications

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Discrete Fourier Transform (DFT) error recovery codes like Reed Solomon codes in the Finite Field are widely used in the communication systems. But the DFT codes in the real and complex fields of numbers are very unstable in the burst of error situations. This paper proposes to change the oversampling patterns in the encoder from the consecutive zero padding to sparse zero padding. It will also prove that the DFT codes based on this type of oversampling are decodable and stable in the case of burst of errors. The simulation results also show the robustness of these codes against quantization error and burst of errors.

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“…Therefore, the singular values of A are the square roots of the eigenvalues of AA H or A H A. These eigenvalues have been studied (a recent reference is [6]), and the results can immediately be applied to A as well.…”

Section: Numerical Stabilitymentioning

confidence: 99%

The stability of a direct method for superresolution

Vieira

Ferreira²

Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181

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A direct method for superresolution recently proposed by Walsh and Delaney is further analyzed from the point of view of numerical stability. The method is based on a set of linear equations Ax = b, where A is m × n, and b is a subset (of cardinal n) of the Fourier transform of the object (which has a total of N samples). We give exact and best possible approximate expressions for the determinant of A, when m = n. As a corollary, it is shown that the smallest eigenvalue of A in absolute value satisfies |λ min | ≤ k(n)N −(n−1)/2 , where k(n) (which is independent of N ) is explicitly given. The magnitude of the smallest eigenvalue of A becomes increasingly small as N grows, even when the number of unknowns n remains constant. When m > n the singular values of A are studied, and related to the eigenvalues of the matrix of two other direct methods. As a result, the connection between the method and the other direct methods is clarified.

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The eigenvalues of matrices that occur in certain interpolation problems

Cited by 20 publications

References 20 publications

A cognitive radio architecture based on sub-Nyquist sampling

A cognitive radio architecture based on sub-Nyquist sampling

Introducing stable oversampling patterns for DFT error recovery codes in bursty erasure channels

The stability of a direct method for superresolution

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