Sampling Theorems for Nonbandlimited Signals

Vaidyanathan, P.P.

doi:10.1007/978-0-8176-8212-5_5

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…1. By exploiting that the derivative ∂P lm (t)/∂t | t=0 of the associated Legendre polynomials on the equator is non-zero exactly for thosem = {m} \ {m} where the function values vanish, we can determine the remaining α lm by derivative sampling, an approach which is in fact well known in the sampling literature [28]. The closure of the derivative under rotation follows from the equivalence with one of the vector Spherical Harmonics basis functions [11,Lemma 12.7.2].…”

Section: Discussionmentioning

confidence: 99%

Efficient and accurate rotation of finite spherical harmonics expansions

Lessig

Witt

Fiume

2012

Journal of Computational Physics

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Spherical harmonics are employed in a wide range of applications in computational science and physics, and many of them require the rotation of functions. We present an efficient and accurate algorithm for the rotation of finite spherical harmonics expansions. Exploiting the pointwise action of the rotation group on functions on the sphere, we obtain the spherical harmonics expansion of a rotated signal from function values at rotated sampling points. The number of sampling points and their location permits one to balance performance and accuracy, making our technique well-suited for a wide range of applications. Numerical experiments comparing different sampling schemes and various techniques from the literature are presented, making this the first thorough evaluation of spherical harmonics rotation algorithms.

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Section: Discussionmentioning

confidence: 99%

Efficient and accurate rotation of finite spherical harmonics expansions

Lessig

Witt

Fiume

2012

Journal of Computational Physics

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“…Interestingly, in [23], a finite number of samples of a filtered signal was used, as opposed to an infinite number of "raw" samples. By the early nineties, the recently arrived wavelet theory [24,25] began to stimulate a strong revival of sampling theory (see, for example, [26,27,28]), by using the mathematics of basis and frames in Hilbert spaces. This framework allowed for the re-formulation of the sampling and reconstruction problem in more general and practical situations, including, inter alia, sampling and reconstruction from finite samples [23,29], study of arbitrary input and reconstruction spaces [11,30,31], sampling of non-band-limited signals [27,10], oversampling [32,33], non-uniform sampling [34,18], filter-banks [35,36], and splines and interpolation [37,38].…”

Section: Historical Notesmentioning

confidence: 99%

“…As will be shown below, depending on the spaces A, S and W, perfect reconstruction can still be possible, even, for example, for non band-limited signals [43,10,27]. In the remainder of this section we will describe conditions on the sampling and reconstruction method which ensure that each of these notions can be achieved.…”

Section: Perfect Reconstructionmentioning

confidence: 99%

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Efficient Data Representations for Signal Processing and Control: "Making Most of a Little"

Goodwin

Derpich

Quevedo

2006

2006 Chinese Control Conference

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Abstract:In order that signals can be stored, transmitted or processed it is necessary that they first be converted into digital form. This, in turn, raises the problem of how to digitize data so as to achieve the best trade-off between data load and performance, i.e., "how to make the most out of a little". Two issues are involved in this problem, namely temporal quantization (i.e., sampling) and spatial quantization. These two problems have traditionally been addressed separately. Indeed, there exists substantial literature dealing with the temporal quantization problem, covering both band-limited and non-band-limited signals. The usual underlying paradigm is that of an analysis filter, followed by a sampler, followed by a reconstruction filter. Various parts of this architecture can be optimized once other parts have been specified. On the other hand, spatial quantization has been studied extensively for a given sampling strategy, particularly in the framework of sigma delta conversion. Finally, it is also possible to formulate the joint design problem for sampling and spatial quantization. This typically leads to enhanced performance compared to that achievable by considering the two aspects separately. This paper will survey the general area of sampling and quantization and analyze methods for achieving efficient data representations for signal processing and control applications. We will show how, on the one hand, contemporary control theory can contribute to the design of sampling and quantization systems and, on the other hand, how these systems impact on the performance of modern feedback control systems.

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Improving accuracy of FIR filters for computing convolution transforms for smooth non-bandlimited signals

Shtrauss

2019

MATEC Web Conf.

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We propose to improve the accuracy of FIR filters for computing convolution transforms for smooth non-bandlimited (NBL) signals by designing filters by the identification method with using a pair of bandlimited portions of the chosen NBL input and output signals related with each other by the given transform. A design example of type IV linear phase differentiator is presented, where filter coefficients are calculated from the bandlimited portions of the Cauchy pulse and its derivative. The performance of the designed differentiator is evaluated by comparing the accuracy of computed derivatives for several smooth NBL test signals, such as the Cauchy pulse, the Hilbert transform of Cauchy pulse, the Gaussian function, as well as for a bandlimited sinc-function. Evaluation results demonstrate that the proposed design method generates more accurate differentiators than the Parks-McClellan algorithm, the impulse response truncation method and the identification with using full-band Cauchy pulse and its derivative.

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Sampling Theorems for Nonbandlimited Signals

Cited by 4 publications

References 24 publications

Efficient and accurate rotation of finite spherical harmonics expansions

Efficient and accurate rotation of finite spherical harmonics expansions

Efficient Data Representations for Signal Processing and Control: "Making Most of a Little"

Improving accuracy of FIR filters for computing convolution transforms for smooth non-bandlimited signals

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