Results 1  10
of
11
Reconstruction of nonuniformly sampled bandlimited signals by means of digital fractional delay filters
 IEEE Trans. Signal Processing
, 2002
"... Abstract – This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The points of departures are that the signal is slightly oversampled as to the average sampling frequency and that the sampling instances are know ..."
Abstract

Cited by 33 (7 self)
 Add to MetaCart
(Show Context)
Abstract – This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The points of departures are that the signal is slightly oversampled as to the average sampling frequency and that the sampling instances are known. Under these assumptions, a representation of the reconstructed sequence is derived that utilizes a timefrequency function. This representation enables a proper utilization of the oversampling and reduces the reconstruction problem to a design problem that resembles an ordinary filter design problem. Furthermore, for an important special case, corresponding to a certain type of periodic nonuniform sampling, it is shown that the reconstruction problem can be posed as a filterbank design problem, thus with requirements on a distortion transfer function and a number of aliasing transfer functions. 1.
Analysis And Design Of MinimaxOptimal Interpolators
 IEEE Trans. Signal Proc
, 1998
"... We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix which is specified for each set of sa ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
(Show Context)
We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix which is specified for each set of sampling points. The error expression can be used to prove that the Yen interpolator is optimal. The implementation of the Yen algorithm suffers from numerical illconditioning, forcing the use of a regularized, approximate solution. We suggest a new, approximate solution, consisting of a sinckernel interpolator with specially chosen weighting coefficients. The newly designed sinckernel interpolator is compared with the usual sinc interpolator using Jacobian (area) weighting, through numerical simulations. We show that the sinc interpolator with Jacobian weighting works well only when the sampling is nearly uniform. The newly designed sinckernel interpolator is shown to perform better than ...
DirectFourier Reconstruction In Tomography And Synthetic Aperture Radar
 Intl. J. Imaging Sys. and Tech
, 1998
"... We investigate the use of directFourier (DF) image reconstruction in computerized tomography and synthetic aperture radar (SAR). One of our aims is to determine why the convolutionbackprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
(Show Context)
We investigate the use of directFourier (DF) image reconstruction in computerized tomography and synthetic aperture radar (SAR). One of our aims is to determine why the convolutionbackprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR. We show that the CBP algorithm is equivalent to DF reconstruction using a Jacobianweighted 2D periodic sinckernel interpolator. This interpolation is not optimal in any sense, which suggests that DF algorithms utilizing optimal interpolators may surpass CBP in image quality. We consider use of two types of DF interpolation: a windowed sinc kernel, and the leastsquares optimal Yen interpolator. Simulations show that reconstructions using the Yen interpolator do not possess the expected visual quality, because of regularization needed to preserve numerical stability. Next, we show that with a concentricsquares sampling scheme, DF interpolation can be performed accurately and efficiently...
Interpolation and denoising of nonuniformly sampled data using wavelet domain processing
 in Proc. IEEE Int. Conf. on Acoust., Speech, Signal Proc.  ICASSP '99
, 1999
"... In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and denoising to derive a suite of multiscale, maximumsmoothness interpolation algorithms. We formulate the interpolation problem as the optimization of finding the signal that matches the given sam ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and denoising to derive a suite of multiscale, maximumsmoothness interpolation algorithms. We formulate the interpolation problem as the optimization of finding the signal that matches the given samples with smallest norm in a function smoothness space. For signals in the Besov space B, " (Lp), the optimization corresponds to convex programming in the wavelet domain; for signals in the Sobolev space We(&), the optimization reduces to a simple weighted leastsquares problem. An optional wavelet shrinkage regularization step makes the algorithm suitable for even noisy sample data, unlike classical approaches such as bandlimited and spline interpolation. 1.
Reconstruction of periodically nonuniformly sampled bandlimited signals using timevarying FIR filters
 In Proc. Fourth Int. Workshop Spectral Methods Multirate Signal Processing
, 2004
"... This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The point of departure is a representation of the reconstructed sequence that utilizes a timefrequency function. This representation enables a proper utiliz ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The point of departure is a representation of the reconstructed sequence that utilizes a timefrequency function. This representation enables a proper utilization of the slight oversampling that is assumed and reduces the reconstruction problem to a design problem that resembles an ordinary filter design problem. Of particular interest in this paper is an important special case of nonuniform sampling that corresponds to a certain type of periodic nonuniform sampling. It is shown how the reconstruction problem in this case can be posed as a multirate filterbank design problem, thus with requirements on a distortion transfer function and a number of aliasing transfer functions. (a) (c) x a(t)
Signal Processing Issues In Synthetic Aperture Radar And Computer Tomography
, 1998
"... ..."
(Show Context)
Analysis and Design of
"... Abstract — We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix that is specified for each ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract — We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix that is specified for each set of sampling points. The error expression can be used to prove that the Yen interpolator is optimal. The implementation of the Yen algorithm suffers from numerical ill conditioning, forcing the use of a regularized, approximate solution. We suggest a new, approximate solution consisting of a sinckernel interpolator with specially chosen weighting coefficients. The newly designed sinckernel interpolator is compared with the usual sinc interpolator using Jacobian (area) weighting through numerical simulations. We show that the sinc interpolator with Jacobian weighting works well only when the sampling is nearly uniform. The newly designed sinckernel interpolator is shown to perform better than the sinc interpolator with Jacobian weighting. I.
INTERPOLATION OF SIGNALS WITH MISSING DATA USING PCA
"... A noniterative methodology for the interpolation of sampled signals with missing data resorting to Principal Component Analysis is introduced. Based on unbiased estimators for the mean and covariance of signals, corrupted by zeromean noise, the Principal Component Analysis is performed and the sig ..."
Abstract
 Add to MetaCart
(Show Context)
A noniterative methodology for the interpolation of sampled signals with missing data resorting to Principal Component Analysis is introduced. Based on unbiased estimators for the mean and covariance of signals, corrupted by zeromean noise, the Principal Component Analysis is performed and the signal is interpolated given the optimal solution of a weighted least squares minimization problem. Upper and lower bounds for the mean square interpolation error are also provided in the interval of validity of the method. A preliminary performance assessment, with 1D and 2D signals, is included based on the results of a series of Monte Carlo experiments. 1.
Statistical Properties of Coded Interlaced and Progressive Image Sequences
"... In the present paper, we investigate the statistical properties of interlaced and progressive image sequences in order to determine what is the most efficient format from a coding point of view. Intra and inter coding modes are both considered. The main result is that, for both intra and inter image ..."
Abstract
 Add to MetaCart
(Show Context)
In the present paper, we investigate the statistical properties of interlaced and progressive image sequences in order to determine what is the most efficient format from a coding point of view. Intra and inter coding modes are both considered. The main result is that, for both intra and inter images, the coding of progressive images outperforms the coding of interlaced ones for low bitrates and large motion vectors. Particular attention is paid to inter coding with subpel accuracy, where the effects of non ideal interpolation filters and finite precision of the motion vector are taken into account. This author would like to thank the Belgian NSF for its financial support 1 Introduction In most present sequence coding algorithms, two categories of images are considered: intra and inter images. This is the case for the popular MPEG 2 coding algorithm [1, 2]. In intra images, no temporal decorrelation is performed. They are used as periodical refresh and as entry points in the sequ...
NonUniform Signaling over BandLimited Channels: A Multirate Signal Processing Approach
"... It is well known that if the communication channel is bandlimited to W Hz one can transmit at most 2W independent symbols per second. Generalized sampling theorems, nevertheless, do not restrict such a signaling to be uniform [1], [2], [3]. That is, it is theoretically possible to distribute the dat ..."
Abstract
 Add to MetaCart
It is well known that if the communication channel is bandlimited to W Hz one can transmit at most 2W independent symbols per second. Generalized sampling theorems, nevertheless, do not restrict such a signaling to be uniform [1], [2], [3]. That is, it is theoretically possible to distribute the data symbols nonuniformly in time as long as the average signaling rate does not exceed 2W. Since the average baud rate remains the same, nonuniform signaling techniques are rarely used in normal communication scenarios. Recently, based on the observation that almost all of the public telephone network is digital, it has been proposed that 56 kb/s transmission is theoretically possible over voice band channels [7]. The proposed signaling is a nonuniform one which makes it possible to receive independent data symbols using available 8 kHz PCM samplers while the average baud rate is kept limited to 7 kbaud (W=3500 Hz). In this report, inspired by the results given in [4], a general frame work f...