Abstract not found

We consider a class of interpolation algorithms, including the least-squares optimal Yen interpolator, and we derive a closed-form 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 ill-conditioning, forcing the use of a regularized, approximate solution. We suggest a new, approximate solution, consisting of a sinc-kernel interpolator with specially chosen weighting coefficients. The newly designed sinc-kernel 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 sinc-kernel interpolator is shown to perform better than ...

Sampling and reconstruction are usually analyzed under the framework of linear signal processing. Powerful tools like the Fourier transform and optimum linear filter design techniques, allow for a very precise analysis of the process. In particular, an optimum linear filter of any length can be derived under most situations. Many of these tools are not available for non-linear systems, and it is usually difficult to find an optimum non-linear system under any criteria. In this paper we analyze the possibility of using non-linear filtering in the interpolation of subsampled images. We show that a very simple (5x5) non-linear reconstruction filter outperforms (for the images analyzed) linear filters of up to 256x256, including optimum (separable) Wiener filters of any size. 1. INTRODUCTION In digital signal processing, it is often necessary to alter the sampling rate of a discrete signal. We usually refer to decimation (or sub-sampling) as the operation of selecting a subset of the or...

In this paper we examine the circumstances under which a discrete-time signal can be exactly interpolated given only every M-th sample. After pointing out the connection between designing an M -fold interpolator and the construction of an M -channel perfect reconstruction filter bank, we derive necessary and sufficient conditions on the signal under which exact interpolation is possible. Bandlimited signals are one obvious example, but numerous others exist. We examine these and show how the interpolators may be constructed. A main application is to iterative interpolation schemes, used for the efficient generation of smooth curves. We show that conventional bandlimited interpolators are not suitable in this context. We illustrate that a better criterion is to use interpolators that are exact for polynomial functions. Further, we demonstrate that these interpolators converge when iterated. We show how these may be designed for any polynomial degree N and any interpolation factor M . Th...

Orthogonal frequency division multiplexing (OFDM) transmitter diversity techniques have been shown to be efficient means of achieving near optimal diversity gain in frequency-selective fading channels. For these systems, knowledge of the channel parameters is required at the receivers for diversity combining and decoding. In this paper, we propose a low complexity, bandwidth efficient, pilotsymbol -assisted channel estimator for multiple transmitter OFDM systems. The pilot symbols are constructed to be non-overlapping in frequency to allow for the simultaneous sounding of the multiple channels. The time-varying channel responses are tracked by interpolating a set of estimates obtained through periodically transmitted pilot symbols. The effectiveness and limitations of the proposed estimator are verified by simulations.

A new technique for blind tracking of fast fading channels in long code CDMA is proposed by exploiting multipath diversity. Based on a linear interpolation channel model, the proposed method blindly identifies a time-varying channel at arbitrary estimating points within a block up to a scale factor and increases bandwidth efficiency allowing only one pilot symbol within a block which is much larger than channel coherence time. The proposed method can be implemented using an efficient state-space inversion technique for multiuser cases. The mean square error performance of the proposed estimator is compared with Cramér-Rao bound for interpolated channel. Modeling error and bit error rate are also evaluated using Monte-Carlo simulations, and compared with the block fading model and a decision-directed tracking technique.

This paper also proposed another reconstruction method based on a direct approximation of the Fourier inversion formula using a twodimensional (2-D) trapezoidal rule. In addition, the possibility of reconstruction from a concentric-squares raster was discussed. Numerous simple interpolators have been tried in DF reconstruction with the results compared with CBP [33]. In [34] and [35], the concept of angular bandlimiting was used to interpolate the polar data onto a Cartesian grid. In [36], a DF reconstruction using bilinear interpolation for diffraction tomography provided image quality that was comparable to that produced by the CBP algorithm. Very good reconstruction quality was obtained in [37] and [38] using a spline interpolator, or a hybrid type of spline interpolator. The notion of "gridding" was introduced in [39] as a method of obtaining optimal inversion of Fourier data. An optimal gridding function was proposed, and successful results were obtained when applied to the tomographic reconstruction problem. In [40], several different gridding functions were tried for DF reconstruction, and the performances were compared. In [41, 42], the linogram reconstruction method was proposed as a form of DF reconstruction. The data collection grid in the linogram method is the same as in the concentric-squares sampling scheme. The inversion of the Fourier data in [41, 42] was accomplished by first applying the chirp-z transform in one direction and then computing FFTs in the other direction. In CT, many of these attempts at DF reconstruction have given a poorer result than the CBP algorithm, due to the error incurred in the process of the polar-to-Cartesian interpolation. The attraction of DF reconstruction, however, is that it is thought to require less computation than ...

. A criterion for designing the class of multirate systems for rate#changing is presented. This criterion arises from a model#matching perspective with maximum relative #

In the last several years, system and integrated circuits (IC) semiconductor industry and research has started refocusing from the general purpose computing platform toward application specific devices and appliances. This shift, compounded with the exponentially growing gap between IC potential and design productivity imposes an urgent need for new design methodologies and technologies. There are four main phases in development of application specific systems (ASS): algorithm, architecture, implementation, and semiconductor realization. The last phase is mainly related to the technology CAD field and is out of main scope of the research presented in this paper.