A Robust Iterative Unfolding Method for Signal Processing

There is a well-known series expansion (Neumann series) in functional analysis for perturbative inversion of specific operators on Banach spaces. However, operators that appear in signal processing (e.g. folding and convolution of probability density functions), in general, do not satisfy the usual convergence condition of that series expansion. This article provides some theorems on the convergence criteria of a similar series expansion for this more general case, which is not covered yet by the literature. The main result is that a series expansion provides a robust unbiased unfolding and deconvolution method. For the case of the deconvolution, such a series expansion can always be applied, and the method always recovers the maximum possible information about the initial probability density function, thus the method is optimal in this sense. A very significant advantage of the presented method is that one does not have to introduce ad hoc frequency regulations etc., as in the case of usual naive deconvolution methods. For the case of general unfolding problems, we present a computer-testable sufficient condition for the convergence of the series expansion in question. Some test examples and physics applications are also given. The most important physics example shall be (which originally motivated our survey on this topic) the case of pi^0 --> gamma+gamma particle decay: we show that one can recover the initial pi^0 momentum density function form the measured single gamma momentum density function by our series expansion.Comment: 23 pages, 9 figure

Data analysis techniques: Spectral processing

The individual steps in the data processing scheme applied to most radars used for wind sounding are analyzed. This processing method uses spectral analysis and assumes a pulse Doppler radar. Improvement in the signal to noise ratio of some radars is discussed

Complex Master Slave Interferometry

A general theoretical model is developed to improve the novel Spectral Domain Interferometry method denoted as Master/Slave (MS) Interferometry. In this model, two functions, g and h are introduced to describe the modulation chirp of the channeled spectrum signal due to nonlinearities in the decoding process from wavenumber to time and due to dispersion in the interferometer. The utilization of these two functions brings two major improvements to previous implementations of the MS method. A first improvement consists in reducing the number of channeled spectra necessary to be collected at Master stage. In previous MSI implementation, the number of channeled spectra at the Master stage equated the number of depths where information was selected from at the Slave stage. The paper demonstrates that two experimental channeled spectra only acquired at Master stage suffice to produce A-scans from any number of resolved depths at the Slave stage. A second improvement is the utilization of complex signal processing. Previous MSI implementations discarded the phase. Complex processing of the electrical signal determined by the channeled spectrum allows phase processing that opens several novel avenues. A first consequence of such signal processing is reduction in the random component of the phase without affecting the axial resolution. In previous MSI implementations, phase instabilities were reduced by an average over the wavenumber that led to reduction in the axial resolution

Power spectral density estimation for wireless fluctuation enhanced gas sensor nodes

Fluctuation enhanced sensing (FES) is a promising method to improve the selectivity and sensitivity of semiconductor and nanotechnology gas sensors. Most measurement setups include high cost signal conditioning and data acquisition units as well as intensive data processing. However, there are attempts to reduce the cost and energy consumption of the hardware and to find efficient processing methods for low cost wireless solutions. In our paper we propose highly efficient signal processing methods to analyze the power spectral density of fluctuations. These support the development of ultra-low-power intelligent fluctuation enhanced wireless sensor nodes while several further applications are also possible

Data processing method for a weak, moving telemetry signal

Method of processing data from a spacecraft, where the carrier has a low signal-to-noise ratio and wide unpredictable frequency shifts, consists of analogue recording of the noisy signal along with a high-frequency tone that is used as a clock to trigger a digitizer