A general framework for developing and evaluating band-limited function extrapolation methods

We consider and analyse sampling theories in the reproducing kernel Hilbert space (RKHS) in this paper. The reconstruction of a function in an RKHS from a given set of sampling points and the reproducing kernel of the RKHS is discussed. Firstly, we analyse and give the optimal approximation of any function belonging to the RKHS in detail. Then, a necessary and sufficient condition to perfectly reconstruct the function in the corresponding RKHS of complex-valued functions is investigated. Based on the derived results, another proof of the sampling theorem in the linear canonical transform (LCT) domain is given. Finally, the optimal approximation of any band-limited function in the LCT domain from infinite sampling points is also analysed and discussed.

Minimum norm reconstruction of band-limited function from regularly or irregularly spaced samples

Electronics Letters ◽

10.1049/el:19890530 ◽

1989 ◽

Vol 25 (12) ◽

pp. 785

Author(s):

D.J. Wingham

Keyword(s):

Minimum Norm ◽

Limited Function ◽

Band Limited ◽

Band Limited Function

Correction to "On the transform property of a band-limited function and its samples"

Proceedings of the IEEE ◽

10.1109/proc.1981.12084 ◽

1981 ◽

Vol 69 (7) ◽

pp. 839-839

Author(s):

A. Erteza ◽

Kun-Shan Lin

Keyword(s):

Limited Function ◽

Band Limited ◽

Band Limited Function

On the transform property of a band-limited function and its samples

Proceedings of the IEEE ◽

10.1109/proc.1980.11887 ◽

1980 ◽

Vol 68 (11) ◽

pp. 1449-1450 ◽

Cited By ~ 1

Author(s):

A. Erteza ◽

Kun-Shan Lin

Keyword(s):

Limited Function ◽

Band Limited ◽

Band Limited Function

Near-Field Warping Sampling Scheme for Broad-Side Antenna Characterization

Electronics ◽

10.3390/electronics9061047 ◽

2020 ◽

Vol 9 (6) ◽

pp. 1047

Author(s):

Maria Maisto ◽

Rocco Pierri ◽

Raffaele Solimene

Keyword(s):

Near Field ◽

Singular Values ◽

Sampling Theorem ◽

Sampling Scheme ◽

Limited Function ◽

Field Radiation ◽

Planar Source ◽

Standard Sampling ◽

Band Limited ◽

Band Limited Function

In this paper the problem of sampling the field radiated by a planar source observed over a finite planar aperture located in the near-field is addressed. The problem is cast as the determination of the spatial measurement positions which allow us to discretize the radiation problem so that the singular values of the radiation operator are well-approximated. More in detail, thanks to a suitably warping transformation of the observation variables, the kernel function of the relevant operator is approximated by a band-limited function and hence the sampling theorem applied to achieved discretization. It results in the sampling points having to be non-linearity arranged across the measurement aperture and their number can be considerably lowered as compared to more standard sampling approach. It is shown that the proposed sampling scheme works well for measurement apertures that are not too large as compared to the source’s size. As a consequence, the method appears better suited for broad-side large antenna whose radiated field is mainly concentrated in front of the antenna. A numerical analysis is included to check the theoretical findings and to study the trade-off between the field accuracy representation (over the measurement aperture) and the truncation error in the estimated far-field radiation pattern.

On determining the unknown band-parameter and truncated sinc series coefficients from a time sampled band-limited function

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.03.110 ◽

2018 ◽

Vol 334 ◽

pp. 60-79

Author(s):

Roy Danchick

Keyword(s):

Band Parameter ◽

Limited Function ◽

Band Limited ◽

Band Limited Function

The reconstruction of a band-limited function and its Fourier transform from a finite number of samples at arbitrary locations by singular value decomposition

IEEE Transactions on Signal Processing ◽

10.1109/78.120799 ◽

1992 ◽

Vol 40 (3) ◽

pp. 559-570 ◽

Cited By ~ 31

Author(s):

D.J. Wingham

Keyword(s):

Fourier Transform ◽

Singular Value Decomposition ◽

Finite Number ◽

Singular Value ◽

Limited Function ◽

Band Limited ◽

Band Limited Function ◽

Value Decomposition

Speech Enhancement Based on EMD and Wavelet Threshold in Noisy Environments

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.989-994.3654 ◽

2014 ◽

Vol 989-994 ◽

pp. 3654-3657

Author(s):

Zi Qin Chen ◽

De Xiang Zhang ◽

Da Ling Yuan

Keyword(s):

Speech Enhancement ◽

Speech Processing ◽

Intrinsic Mode Functions ◽

Noisy Environments ◽

Mode Decomposition ◽

Limited Function ◽

Band Limited ◽

A New Technique ◽

Band Limited Function ◽

Target Characteristics

Speech enhancement is crucial for speech recognition accuracy. How to eliminate the effect of the noise constitutes a challenging problem in speech processing. This paper presents a new technique for speech enhancement in a noisy environment based on the empirical mode decomposition (EMD) algorithm and wavelet threshold. With the EMD, the noise speech signals can be decomposed into a sum of the band-limited function called intrinsic mode functions (IMFs), which is a zero-mean AM-FM component. Then wavelet threshold of the IMF components can be used to eliminate the effect of the noise for speech enhancement. Experimental results show that the proposed speech enhancement by de-noising algorithm is possible to achieve an excellent balance between suppresses noise effectively and preserves as many target characteristics of original signal as possible.