Sampling based on local bandwidth

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 105-106).The sampling of continuous-time signals based on local bandwidth is considered in this thesis. In an intuitive sense, local bandwidth refers to the rate at which a signal varies locally. One would expect that signals should be sampled at a higher rate in regions of higher local bandwidth, and at a lower rate in regions of lower local bandwidth. In many cases, sampling signals based on local bandwidth can yield more efficient representations as compared with conventional uniform sampling, which does not exploit local signal characteristics. In the first part of the thesis, a particular definition for a linear time-varying lowpass filter is adopted as a potential model for local bandwidth. A sampling and reconstruction method permitting consistent resampling is developed for signals generated by such filters. The method does not generally result in perfect reconstruction except for a special class of self-similar signals. However, the reconstruction error is shown to decrease with the variation in the cut-off frequency of the filter. In the second part of the thesis, a definition for local bandwidth based on the time-warping of globally bandlimited signals is reviewed. Using this definition, a method is developed for sampling and reconstructing signals according to local bandwidth. The method employs a time-warping to minimize the energy of a signal above a given maximum frequency. A number of techniques for determining the optimal time-warping are examined.by Dennis Wei.M.Eng

Time Delay Estimation from Low Rate Samples: A Union of Subspaces Approach

Time delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel. Various approaches have been proposed in the literature to identify time delays introduced by multipath environments. However, these methods either operate on the analog received signal, or require high sampling rates in order to achieve reasonable time resolution. In this paper, our goal is to develop a unified approach to time delay estimation from low rate samples of the output of a multipath channel. Our methods result in perfect recovery of the multipath delays from samples of the channel output at the lowest possible rate, even in the presence of overlapping transmitted pulses. This rate depends only on the number of multipath components and the transmission rate, but not on the bandwidth of the probing signal. In addition, our development allows for a variety of different sampling methods. By properly manipulating the low-rate samples, we show that the time delays can be recovered using the well-known ESPRIT algorithm. Combining results from sampling theory with those obtained in the context of direction of arrival estimation methods, we develop necessary and sufficient conditions on the transmitted pulse and the sampling functions in order to ensure perfect recovery of the channel parameters at the minimal possible rate. Our results can be viewed in a broader context, as a sampling theorem for analog signals defined over an infinite union of subspaces

Reduced bandwidth video communication system utilizing sampling techniques Patent

Monitoring circuit design for sampling circuit control and reduction of time-bandwidth in video communication system

From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then lowpass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, realtime performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.Comment: 17 pages, 12 figures, to appear in IEEE Journal of Selected Topics in Signal Processing, the special issue on Compressed Sensin

Measuring dynamic signals with direct sensor-to-microcontroller interfaces applied to a magnetoresistive sensor

This paper evaluates the performance of direct interface circuits (DIC), where the sensor is directly connected to a microcontroller, when a resistive sensor subjected to dynamic changes is measured. The theoretical analysis provides guidelines for the selection of the components taking into account both the desired resolution and the bandwidth of the input signal. Such an analysis reveals that there is a trade-off between the sampling frequency and the resolution of the measurement, and this depends on the selected value of the capacitor that forms the RC circuit together with the sensor resistance. This performance is then experimentally proved with a DIC measuring a magnetoresistive sensor exposed to a magnetic field of different frequencies, amplitudes, and waveforms. A sinusoidal magnetic field up to 1 kHz can be monitored with a resolution of eight bits and a sampling frequency of around 10 kSa/s. If a higher resolution is desired, the sampling frequency has to be lower, thus limiting the bandwidth of the dynamic signal under measurement. The DIC is also applied to measure an electrocardiogram-type signal and its QRS complex is well identified, which enables the estimation, for instance, of the heart rate.Postprint (published version

Distributed Adaptive Learning of Graph Signals

The aim of this paper is to propose distributed strategies for adaptive learning of signals defined over graphs. Assuming the graph signal to be bandlimited, the method enables distributed reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of sampled observations taken from a subset of vertices. A detailed mean square analysis is carried out and illustrates the role played by the sampling strategy on the performance of the proposed method. Finally, some useful strategies for distributed selection of the sampling set are provided. Several numerical results validate our theoretical findings, and illustrate the performance of the proposed method for distributed adaptive learning of signals defined over graphs.Comment: To appear in IEEE Transactions on Signal Processing, 201

Sampling and Reconstruction of Spatial Fields using Mobile Sensors

Spatial sampling is traditionally studied in a static setting where static sensors scattered around space take measurements of the spatial field at their locations. In this paper we study the emerging paradigm of sampling and reconstructing spatial fields using sensors that move through space. We show that mobile sensing offers some unique advantages over static sensing in sensing time-invariant bandlimited spatial fields. Since a moving sensor encounters such a spatial field along its path as a time-domain signal, a time-domain anti-aliasing filter can be employed prior to sampling the signal received at the sensor. Such a filtering procedure, when used by a configuration of sensors moving at constant speeds along equispaced parallel lines, leads to a complete suppression of spatial aliasing in the direction of motion of the sensors. We analytically quantify the advantage of using such a sampling scheme over a static sampling scheme by computing the reduction in sampling noise due to the filter. We also analyze the effects of non-uniform sensor speeds on the reconstruction accuracy. Using simulation examples we demonstrate the advantages of mobile sampling over static sampling in practical problems. We extend our analysis to sampling and reconstruction schemes for monitoring time-varying bandlimited fields using mobile sensors. We demonstrate that in some situations we require a lower density of sensors when using a mobile sensing scheme instead of the conventional static sensing scheme. The exact advantage is quantified for a problem of sampling and reconstructing an audio field.Comment: Submitted to IEEE Transactions on Signal Processing May 2012; revised Oct 201