Sampling (signal processing)

About: Sampling (signal processing) is a research topic. Over the lifetime, 26855 publications have been published within this topic receiving 218111 citations.

Multirate digital signal processing

Abstract: There has been a great deal of material in the area of discrete-time transforms that has been published in recent years. This book does an excellent job of presenting important aspects of such material in a clear manner. The book has 11 chapters and a very useful appendix. Seven of these chapters are essentially devoted to the Fourier series/transform, discrete Fourier transform, fast Fourier transform (FFT), and applications of the FFT in the area of spectral estimation. Chapters 8 through 10 deal with many other discrete-time transforms and algorithms to compute them. Of these transforms, the KarhunenLoeve, the discrete cosine, and the Walsh-Hadamard transform are perhaps the most well-known. A lucid discussion of number theoretic transforms i5 presented in Chapter 11. This reviewer feels that the authors have done a fine job of compiling the pertinent material and presenting it in a concise and clear manner. There are a number of problems at the end of each chapter, an appreciable number of which are challenging. The authors have included a comprehensive set of references at the end of the book. In brief, this book is a valuable contribution to the general areas of signal processing and communications. It can be used for a graduate level course in perhaps two ways. One would be to cover the first seven chapters in great detail. The other would be to cover the whole book by focussing on different topics in a selective manner. This book by Elliott and Rao is extremely useful to researchers/engineers who are working in the areas of signal processing and communications. It i s also an excellent reference book, and hence a valuable addition to one’s library

Stochastic sampling in computer graphics

Abstract: Ray tracing, ray casting, and other forms of point sampling are important techniques in computer graphics, but their usefulness has been undermined by aliasing artifacts. In this paper it is shown that these artifacts are not an inherent part of point sampling, but a consequence of using regularly spaced samples. If the samples occur at appropriate nonuniformly spaced locations, frequencies above the Nyquist limit do not alias, but instead appear as noise of the correct average intensity. This noise is much less objectionable to our visual system than aliasing. In ray tracing, the rays can be stochastically distributed to perform a Monte Carlo evaluation of integrals in the rendering equation. This is called distributed ray tracing and can be used to simulate motion blur, depth of field, penumbrae, gloss, and translucency.

Plenoptic sampling

Abstract: This paper studies the problem of plenoptic sampling in image-based rendering (IBR). From a spectral analysis of light field signals and using the sampling theorem, we mathematically derive the analytical functions to determine the minimum sampling rate for light field rendering. The spectral support of a light field signal is bounded by the minimum and maximum depths only, no matter how complicated the spectral support might be because of depth variations in the scene. The minimum sampling rate for light field rendering is obtained by compacting the replicas of the spectral support of the sampled light field within the smallest interval. Given the minimum and maximum depths, a reconstruction filter with an optimal and constant depth can be designed to achieve anti-aliased light field rendering.Plenoptic sampling goes beyond the minimum number of images needed for anti-aliased light field rendering. More significantly, it utilizes the scene depth information to determine the minimum sampling curve in the joint image and geometry space. The minimum sampling curve quantitatively describes the relationship among three key elements in IBR systems: scene complexity (geometrical and textural information), the number of image samples, and the output resolution. Therefore, plenoptic sampling bridges the gap between image-based rendering and traditional geometry-based rendering. Experimental results demonstrate the effectiveness of our approach.

Blind Multi-Band Signal Reconstruction: Compressed Sensing for Analog Signals

Abstract: We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the band locations. In this paper, we develop a non-linear blind perfect reconstruction scheme for multi-band signals which does not require the band locations. Our approach assumes an existing blind multi-coset sampling method. The sparse structure of multi-band signals in the continuous frequency domain is used to replace the continuous reconstruction with a single finite dimensional problem without the need for discretization. The resulting problem can be formulated within the framework of compressed sensing, and thus can be solved efficiently using known tractable algorithms from this emerging area. We also develop a theoretical lower bound on the average sampling rate required for blind signal reconstruction, which is twice the minimal rate of known-spectrum recovery. Our method ensures perfect reconstruction for a wide class of signals sampled at the minimal rate. Numerical experiments are presented demonstrating blind sampling and reconstruction with minimal sampling rate.