Non-uniform Sampling Theory Research Articles

A Digital Predistortion for Concurrent Dual-Band Power Amplifier Linearization Based on Periodically Nonuniform Sampling Theory

In this article, we propose a novel technique of digital predistortion (DPD) for dual-band power amplifiers (PAs) based on the periodically nonuniform sampling (PNS) theory. In contrast to conventional dual-band DPD (2-D-DPD) models, the proposed periodically nonuniform sampled DPD (PNS-DPD) has only a single input, which can largely reduce the model complexity. We fold the two stimuli with aliasing and feed them to a simple single-band DPD model. The desired predistorted signals are reconstructed from aliased DPD output through the PNS theory. Compared with conventional multi-input models that include numerous intermodulation products of the input signals, the complexity of the proposed single-input PNS-DPD model is hugely decreased. The model coefficients of the proposed PNS-DPD can be easily extracted with conventional direct or indirect learning architecture. We experimentally evaluate the proposed DPD on a test bench and compare it with other DPD techniques in the literature. The implementation complexity can be reduced by over 30%, and the identification complexity is also largely reduced.

The Automatic Proportionator Estimator Is Highly Efficient for Estimation of Total Number of Sparse Cell Populations.

Estimation of total number of a population of cells that are sparsely distributed in an organ or anatomically-defined region of interest represents a challenge for conventional stereological methods. In these situations, classic fractionator approaches that rely on systematic uniform random sampling are highly inefficient and, in many cases, impractical due to the intense sampling of the organ and tissue sections that is required to obtain sufficient counts for an acceptable level of precision. The proportionator, an estimator based on non-uniform sampling theory, marries automated image analysis with stereological principles and is the only estimator that provides a highly efficient and precise method to address these challenging quantification problems. In this paper, the practical considerations of the proportionator estimator and its implementation with Proportionator™ software and digital slide imaging are reviewed. The power of the proportionator as a stereological tool is illustrated in its application to the estimation of the total number of a very rare (~50/vertebrae) and sparsely distributed population of osteoprogenitor cells in mouse vertebral body. The proportionator offers a solution to neuroscientists interested in quantifying total cell number of sparse cell populations in the central and peripheral nervous system where systematic uniform random sampling-based stereological estimators are impractical.

Modifications on Multichannel Reconstruction Algorithm for SAR Processing Based on Periodic Nonuniform Sampling Theory and Nonuniform Fast Fourier Transform

The next generation of space-borne synthetic aperture radar (SAR) systems will emphasize on high-resolution and wide-swath imaging. For these design goals, multichannel technology in azimuth is a promising candidate and can provide global monitoring capacity for the continuous observation of a highly dynamic and rapidly changing world with high spatial resolution and short repeat intervals. In the multichannel SAR system, the nonuniform azimuth signal needs to be reconstructed when the pulse repetition frequency is different from a specific one. A reconstruction algorithm based on periodic nonuniform sampling theory has been proposed in current literature, but it is computationally rather expensive. In this paper, nonuniform fast Fourier transform is employed to reduce the computation load of the original algorithm from $O(N^2) $ to $O(N\log N) $ , where $N$ is azimuth sample number. Furthermore, a modification is implemented by taking the out-of-band energy into account to suppress the azimuth ambiguity when the signal is not band-limited, which is actually the case of the azimuth modulation of SAR with a real antenna pattern. The computation and reconstruction performances validate the proposed method’s effectiveness in multichannel signal processing and its suppression effect on azimuth ambiguity.

A Novel Reconstruction Framework for Time-Encoded Signals with Integrate-and-Fire Neurons.

Integrate-and-fire neurons are time encoding machines that convert the amplitude of an analog signal into a nonuniform, strictly increasing sequence of spike times. Under certain conditions, the encoded signals can be reconstructed from the nonuniform spike time sequences using a time decoding machine. Time encoding and time decoding methods have been studied using the nonuniform sampling theory for band-limited spaces, as well as for generic shift-invariant spaces. This letter proposes a new framework for studying IF time encoding and decoding by reformulating the IF time encoding problem as a uniform sampling problem. This framework forms the basis for two new algorithms for reconstructing signals from spike time sequences. We demonstrate that the proposed reconstruction algorithms are faster, and thus better suited for real-time processing, while providing a similar level of accuracy, compared to the standard reconstruction algorithm.

A novel recovery algorithm of time encoded signals

The integrate-and-fire (IAF) neuron model is a Time Encoding Machine (TEM), which maps analog signals into a sequence of strictly increasing time events. There are a number of reconstruction algorithms that ensure perfect recovery of bandlimited input signals from spike trains [1]. For signals that are not bandlimited, or when their bandwidth is unknown, the algorithms available [2] ensure that the reconstructed signal satisfies a consistency constraint, i.e., the reconstructed stimulus generates the same spike train as the original stimulus. As noted in [2], consistent reconstruction is more relevant and useful for recovering real sensory stimuli because a good estimate of the bandwidth is often not available. The existing algorithms that reconstruct the inputs encoded with TEMs exploit, in some form, the nonuniform sampling theory. Here we propose a novel consistent algorithm for signal reconstruction from spike trains, which involves solving an associated interpolation problem based on uniformly sampled data, and present theoretical results that underpin the proposed reconstruction method. While providing similar accuracy, our algorithm is faster and thus better suited for real-time processing, because our approach does not require recalculating the basis functions used in reconstruction for different sets of spikes. In addition, the new approach provides an alternative framework to study spike processing. To show the performance of our algorithm, we compared it to the best consistent reconstruction method available [2]. The input used was a periodic signal with randomly generated Fourier coefficients. The computation time and reconstruction accuracy of each algorithm were evaluated for 100 randomly generated input sequences. The estimated probability density functions corresponding to each performance index are shown in Figures 1A&B. The average computation time, plotted as a function of the number of spikes (Figure ​(Figure1B),1B), demonstrates that computing time is almost independent on the number of spikes. The simulations were carried out in Matlab on a 3.10 GHz Intel Single Core PC workstation. Figure 1 Reconstruction performance comparison: A - computing time, B - accuracy (SNR), C - computation time as function of the number of spikes used in reconstruction.

A comparison of motion-compensated interlace-to-progressive conversion methods

The conversion of interlaced video to progressive format may be carried out in a number of ways, including vertical interpolation, fixed or motion-compensated vertical-temporal interpolation, and approaches based on motion compensation using non-uniform sampling theory. Motion-compensated methods potentially offer the best performance, although the accuracy and reliability of the vectors has a significant impact on their performance. For applications such as display conversion using vectors recovered from an MPEG-2 bitstream, the vectors available may not be of the highest quality. This paper considers several motion-compensated interlace-to-progressive conversion methods, and assesses their performance with both accurate and inaccurate vectors using objective and subjective techniques. The method found to work best uses a motion-compensated three-field vertical-temporal filter, in which the vertical component of the vector is rounded to the nearest even number of picture lines per field period. This method reduced the RMS error of converted picture sequences by almost 20% compared to simple vertical filtering when using vectors from an MPEG-2 bitstream. Conversely, some other motion-compensated methods were found to increase the error by a similar amount.

Efficient numerical methods in non-uniform sampling theory

Summary. We present a new “second generation” reconstruction algorithm for irregular sampling, i.e. for the problem of recovering a band-limited function from its non-uniformly sampled values. The efficient new method is a combination of the adaptive weights method which was developed by the two first named authors and the method of conjugate gradients for the solution of positive definite linear systems. The choice of ”adaptive weights” can be seen as a simple but very efficient method of preconditioning. Further substantial acceleration is achieved by utilizing the Toeplitztype structure of the system matrix. This new algorithm can handle problems of much larger dimension and condition number than have been accessible so far. Furthermore, if some gaps between samples are large, then the algorithm can still be used as a very efficient extrapolation method across the gaps.