Repeated random sampling in year 5

As an extension to an activity introducing Year 5 students to the practice of statistics, the software TinkerPlots made it possible to collect repeated random samples from a finite population to informally explore students’ capacity to begin reasoning with a distribution of sample statistics. This article provides background for the sampling process and reports on the success of students in making predictions for the population from the collection of simulated samples and in explaining their strategies. The activity provided an application of the numeracy skill of using percentages, the numerical summary of the data, rather than graphing data in the analysis of samples to make decisions on a statistical question. About 70% of students made what were considered at least moderately good predictions of the population percentages for five yes–no questions, and the correlation between predictions and explanations was 0.78.

A novel fractional sampling offset estimation in an OFDM system

The Orthogonal Frequency Division Multiplexing (OFDM) is a form of Multi-Carrier Modulation where the data stream is transmitted over a number of carriers which are orthogonal to each other i.e. the carrier spacing is selected such that each carrier is located at the zeroes of all other carriers in the spectral domain. This paper proposes a new novel sampling offset estimation algorithm for an OFDM system in order to receive the OFDM data symbols error-free over the noisy channel at the receiver and to achieve fine timing synchronization between the transmitter and the receiver. The performance of this algorithm has been studied in AWGN, ADSL and SUI channels successfully.

A novel fractional sampling offset estimation in an OFDM system

The Orthogonal Frequency Division Multiplexing (OFDM) is a form of Multi-Carrier Modulation where the data stream is transmitted over a number of carriers which are orthogonal to each other i.e. the carrier spacing is selected such that each carrier is located at the zeroes of all other carriers in the spectral domain. This paper proposes a new novel sampling offset estimation algorithm for an OFDM system in order to receive the OFDM data symbols error-free over the noisy channel at the receiver and to achieve fine timing synchronization between the transmitter and the receiver. The performance of this algorithm has been studied in AWGN, ADSL and SUI channels successfully.

Novel Approaches to the Sampling of Atmospheric Aerosols and Determination of Chemical Composition

The Earth s climate is a highly dynamic and complex system in which atmospheric aerosols have been increasingly recognized to play a key role. Aerosol particles affect the climate through a multitude of processes, directly by absorbing and reflecting radiation and indirectly by changing the properties of clouds. Because of the complexity, quantification of the effects of aerosols continues to be a highly uncertain science. Better understanding of the effects of aerosols requires more information on aerosol chemistry. Before the determination of aerosol chemical composition by the various available analytical techniques, aerosol particles must be reliably sampled and prepared. Indeed, sampling is one of the most challenging steps in aerosol studies, since all available sampling techniques harbor drawbacks. In this study, novel methodologies were developed for sampling and determination of the chemical composition of atmospheric aerosols. In the particle-into-liquid sampler (PILS), aerosol particles grow in saturated water vapor with further impaction and dissolution in liquid water. Once in water, the aerosol sample can then be transported and analyzed by various off-line or on-line techniques. In this study, PILS was modified and the sampling procedure was optimized to obtain less altered aerosol samples with good time resolution. A combination of denuders with different coatings was tested to adsorb gas phase compounds before PILS. Mixtures of water with alcohols were introduced to increase the solubility of aerosols. Minimum sampling time required was determined by collecting samples off-line every hour and proceeding with liquid-liquid extraction (LLE) and analysis by gas chromatography-mass spectrometry (GC-MS). The laboriousness of LLE followed by GC-MS analysis next prompted an evaluation of solid-phase extraction (SPE) for the extraction of aldehydes and acids in aerosol samples. These two compound groups are thought to be key for aerosol growth. Octadecylsilica, hydrophilic-lipophilic balance (HLB), and mixed phase anion exchange (MAX) were tested as extraction materials. MAX proved to be efficient for acids, but no tested material offered sufficient adsorption for aldehydes. Thus, PILS samples were extracted only with MAX to guarantee good results for organic acids determined by liquid chromatography-mass spectrometry (HPLC-MS). On-line coupling of SPE with HPLC-MS is relatively easy, and here on-line coupling of PILS with HPLC-MS through the SPE trap produced some interesting data on relevant acids in atmospheric aerosol samples. A completely different approach to aerosol sampling, namely, differential mobility analyzer (DMA)-assisted filter sampling, was employed in this study to provide information about the size dependent chemical composition of aerosols and understanding of the processes driving aerosol growth from nano-size clusters to climatically relevant particles (>40 nm). The DMA was set to sample particles with diameters of 50, 40, and 30 nm and aerosols were collected on teflon or quartz fiber filters. To clarify the gas-phase contribution, zero gas-phase samples were collected by switching off the DMA every other 15 minutes. Gas-phase compounds were adsorbed equally well on both types of filter, and were found to contribute significantly to the total compound mass. Gas-phase adsorption is especially significant during the collection of nanometer-size aerosols and needs always to be taken into account. Other aims of this study were to determine the oxidation products of β-caryophyllene (the major sesquiterpene in boreal forest) in aerosol particles. Since reference compounds are needed for verification of the accuracy of analytical measurements, three oxidation products of β-caryophyllene were synthesized: β-caryophyllene aldehyde, β-nocaryophyllene aldehyde, and β-caryophyllinic acid. All three were identified for the first time in ambient aerosol samples, at relatively high concentrations, and their contribution to the aerosol mass (and probably growth) was concluded to be significant. Methodological and instrumental developments presented in this work enable fuller understanding of the processes behind biogenic aerosol formation and provide new tools for more precise determination of biosphere-atmosphere interactions.

Influence of sampling frequency on the estimates of runoff water quality

Tiivistelmä: Havaintotiheyden vaikutus valumavesien laatuarvioihin

A Sub-Nyquist Sampling Method For Computing The Level-crossing-times Of An Analog Signal: Theory And Applications

We address the problem of computing the level-crossings of an analog signal from samples measured on a uniform grid. Such a problem is important, for example, in multilevel analog-to-digital (A/D) converters. The first operation in such sampling modalities is a comparator, which gives rise to a bilevel waveform. Since bilevel signals are not bandlimited, measuring the level-crossing times exactly becomes impractical within the conventional framework of Shannon sampling. In this paper, we propose a novel sub-Nyquist sampling technique for making measurements on a uniform grid and thereby for exactly computing the level-crossing times from those samples. The computational complexity of the technique is low and comprises simple arithmetic operations. We also present a finite-rate-of-innovation sampling perspective of the proposed approach and also show how exponential splines fit in naturally into the proposed sampling framework. We also discuss some concrete practical applications of the sampling technique.

An Efficient Random Walk Strategy for Sampling Based Robot Motion Planners

Sampling based planners have been successful in path planning of robots with many degrees of freedom, but still remains ineffective when the configuration space has a narrow passage. We present a new technique based on a random walk strategy to generate samples in narrow regions quickly, thus improving efficiency of Probabilistic Roadmap Planners. The algorithm substantially reduces instances of collision checking and thereby decreases computational time. The method is powerful even for cases where the structure of the narrow passage is not known, thus giving significant improvement over other known methods.

Sampling disturbances of soft sensitive clays

Sampling disturbance is unavoidable and hence the laboratory testing most often is on partially disturbed samples. This paper deals with the development of a simple method to assess degree of sample disturbance from the prediction of yield stress due to cementation and comparison of yield stress in compression of partially disturbed sample with reference to a predicted compression path of the clay devoid of any mechanical disturbance. The method uses simple parameters which are normally determined in routine investigations.

A finite-rate-of-innovation signal sampling perspective of the source-filter model of speech production

We consider the speech production mechanism and the asso- ciated linear source-filter model. For voiced speech sounds in particular, the source/glottal excitation is modeled as a stream of impulses and the filter as a cascade of second-order resonators. We show that the process of sampling speech signals can be modeled as filtering a stream of Dirac impulses (a model for the excitation) with a kernel function (the vocal tract response),and then sampling uniformly. We show that the problem of esti- mating the excitation is equivalent to the problem of recovering a stream of Dirac impulses from samples of a filtered version. We present associated algorithms based on the annihilating filter and also make a comparison with the classical linear prediction technique, which is well known in speech analysis. Results on synthesized as well as natural speech data are presented.

On Selection of Search Space Dimension in Compressive Sampling Matching Pursuit

Compressive Sampling Matching Pursuit (CoSaMP) is one of the popular greedy methods in the emerging field of Compressed Sensing (CS). In addition to the appealing empirical performance, CoSaMP has also splendid theoretical guarantees for convergence. In this paper, we propose a modification in CoSaMP to adaptively choose the dimension of search space in each iteration, using a threshold based approach. Using Monte Carlo simulations, we show that this modification improves the reconstruction capability of the CoSaMP algorithm in clean as well as noisy measurement cases. From empirical observations, we also propose an optimum value for the threshold to use in applications.

A multichannel sampling method for 2-D finite-rate-of-innovation signals

We address the problem of sampling and reconstruction of two-dimensional (2-D) finite-rate-of-innovation (FRI) signals. We propose a three-channel sampling method for efficiently solving the problem. We consider the sampling of a stream of 2-D Dirac impulses and a sum of 2-D unit-step functions. We propose a 2-D causal exponential function as the sampling kernel. By causality in 2-D, we mean that the function has its support restricted to the first quadrant. The advantage of using a multichannel sampling method with causal exponential sampling kernel is that standard annihilating filter or root-finding algorithms are not required. Further, the proposed method has inexpensive hardware implementation and is numerically stable as the number of Dirac impulses increases.

A Novel Monte-Carlo-Sampling-Based Receiver for Large-Scale Uplink Multiuser MIMO Systems

In this paper, we propose low-complexity algorithms based on Monte Carlo sampling for signal detection and channel estimation on the uplink in large-scale multiuser multiple-input-multiple-output (MIMO) systems with tens to hundreds of antennas at the base station (BS) and a similar number of uplink users. A BS receiver that employs a novel mixed sampling technique (which makes a probabilistic choice between Gibbs sampling and random uniform sampling in each coordinate update) for detection and a Gibbs-sampling-based method for channel estimation is proposed. The algorithm proposed for detection alleviates the stalling problem encountered at high signal-to-noise ratios (SNRs) in conventional Gibbs-sampling-based detection and achieves near-optimal performance in large systems with M-ary quadrature amplitude modulation (M-QAM). A novel ingredient in the detection algorithm that is responsible for achieving near-optimal performance at low complexity is the joint use of a mixed Gibbs sampling (MGS) strategy coupled with a multiple restart (MR) strategy with an efficient restart criterion. Near-optimal detection performance is demonstrated for a large number of BS antennas and users (e. g., 64 and 128 BS antennas and users). The proposed Gibbs-sampling-based channel estimation algorithm refines an initial estimate of the channel obtained during the pilot phase through iterations with the proposed MGS-based detection during the data phase. In time-division duplex systems where channel reciprocity holds, these channel estimates can be used for multiuser MIMO precoding on the downlink. The proposed receiver is shown to achieve good performance and scale well for large dimensions.

Group testing based spectrum hole search using a simple sub-nyquist sampling scheme

In this paper, we consider the problem of finding a spectrum hole of a specified bandwidth in a given wide band of interest. We propose a new, simple and easily implementable sub-Nyquist sampling scheme for signal acquisition and a spectrum hole search algorithm that exploits sparsity in the primary spectral occupancy in the frequency domain by testing a group of adjacent subbands in a single test. The sampling scheme deliberately introduces aliasing during signal acquisition, resulting in a signal that is the sum of signals from adjacent sub-bands. Energy-based hypothesis tests are used to provide an occupancy decision over the group of subbands, and this forms the basis of the proposed algorithm to find contiguous spectrum holes. We extend this framework to a multi-stage sensing algorithm that can be employed in a variety of spectrum sensing scenarios, including non-contiguous spectrum hole search. Further, we provide the analytical means to optimize the hypothesis tests with respect to the detection thresholds, number of samples and group size to minimize the detection delay under a given error rate constraint. Depending on the sparsity and SNR, the proposed algorithms can lead to significantly lower detection delays compared to a conventional bin-by-bin energy detection scheme; the latter is in fact a special case of the group test when the group size is set to 1. We validate our analytical results via Monte Carlo simulations.