Interpolation and the discrete Papoulis-Gerchberg algorithm

Ferreira, Paulo J. S. G.

doi:10.1109/78.324726

Cited by 102 publications

(72 citation statements)

References 57 publications

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“…We show that uniform sampling results in the most stable and simple reconstruction algorithm. We note that similar results were derived in [21] for iterative reconstruction methods of periodic bandlimited signals. Recurrent nonuniform sampling is of interest in digital signal processing due to its ability to represent the sampling process as a bank of digital-to-analog (D-to-A) converters [22].…”

supporting

confidence: 56%

Nonuniform Sampling of Periodic Bandlimited Signals

Margolis

Eldar

2008

IEEE Trans. Signal Process.

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Abstract-Digital processing techniques are based on representing a continuous-time signal by a discrete set of samples. This paper treats the problem of reconstructing a periodic bandlimited signal from a finite number of its nonuniform samples. In practical applications, only a finite number of values are given. Extending the samples periodically across the boundaries, and assuming that the underlying continuous time signal is bandlimited, provides a simple way to deal with reconstruction from finitely many samples. Two algorithms for reconstructing a periodic bandlimited signal from an even and an odd number of nonuniform samples are developed. In the first, the reconstruction functions constitute a basis while in the second, they form a frame so that there are more samples than needed for perfect reconstruction. The advantages and disadvantages of each method are analyzed. Specifically, it is shown that the first algorithm provides consistent reconstruction of the signal while the second is shown to be more stable in noisy environments. Next, we use the theory of finite dimensional frames to characterize the stability of our algorithms. We then consider two special distributions of sampling points: uniform and recurrent nonuniform, and show that for these cases, the reconstruction formulas as well as the stability analysis are simplified significantly. The advantage of our methods over conventional approaches is demonstrated by numerical experiments.

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supporting

confidence: 56%

Nonuniform Sampling of Periodic Bandlimited Signals

Margolis

Eldar

2008

IEEE Trans. Signal Process.

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“…In (Ferreira, 1994a) it is demonstrated that the algorithm converges if both conditions are satisfied: 0<<2 and 2 1 Equation (12). Because we have considered =1 and used low pass signals the iterative process converges.…”

Section: Convergence Analysismentioning

confidence: 99%

“…Despite the fact of having an ill conditioned problem, in direct calculation method such problem is impossible to solve whereas in iterative methods an approximation is always possible to be found, though its accuracy may not be very high. The conditions under which these equations provide a solution for u can be found in (Ferreira, 1994a) and will be discussed in the next subsection.…”

Section: Minimum Dimention Algorithmmentioning

confidence: 99%

“…It is demonstrated in (Ferreira, 1994a) that for low pass signals of dimension n with s known samples and q nonzero harmonics, reconstruction iterative algorithm converges if:…”

Section: Convergence Analysismentioning

confidence: 99%

“…The signal reconstruction algorithm used in SPIEW was the discrete version of the Papoulis algorithm (Papoulis, 1975): the Papoulis Gerchberg algorithm (Ferreira, 1994a;Jones, 1986). A thorough description of this maximum dimension algorithm can be found in (Costa et al, 2012).…”

Section: Reconstruction Algorithmsmentioning

confidence: 99%

See 2 more Smart Citations

Signal Processing Interpolation and Problem Conditioning Educational Workbench

Costa¹,

Soares²,

Barroso³

2013

MAS

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This work presents a newer and more complete version of an educational tool to be used in signal processing interpolation-related subjects. Besides the consolidation of acquired theoretical knowledge, the tool allows now its users to apply three error geometry patterns, test minimum or maximum dimension signal reconstruction algorithms and problem conditioning through the analysis of the matrix spectral radius or the condition number: these new features gives the possibility to alter the problem definitions to the desired goal before the reconstruction begins. The time unit that measures the algorithms performance is (nlogn) thus independent from the machine's architecture. A video of the developed tool can be seen in: https://www.dropbox.com/s/t6yiiuy31ramxse/FILME_1.avi.

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Signal and image reconstruction in undergraduate education: Tools for assessing and comparing a set of algorithms

Reis

Ferreira

2004

Comput. Appl. Eng. Educ.

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This paper discusses signal and image reconstruction in connection with undergraduate electrical engineering education. It briefly reviews some of the basic signal and image reconstruction techniques, and presents two Java applets that have been found useful in the context. The applets have easy-to-use, friendly interfaces, and can be used as tools to teach reconstruction techniques or as a laboratory to study the applicability of the methods to real world signals and images. The students can do simulations with their own data (signals or images) on any computer platform.

show abstract

Interpolation and the discrete Papoulis-Gerchberg algorithm

Cited by 102 publications

References 57 publications

Nonuniform Sampling of Periodic Bandlimited Signals

Nonuniform Sampling of Periodic Bandlimited Signals

Signal Processing Interpolation and Problem Conditioning Educational Workbench

Signal and image reconstruction in undergraduate education: Tools for assessing and comparing a set of algorithms

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