Coherent Line Removal: Filtering out harmonically related line interference from experimental data, with application to gravitational wave detectors

We describe a new technique for removing troublesome interference from external coherent signals present in the gravitational wave spectrum. The method works when the interference is present in many harmonics, as long as they remain coherent with one another. The method can remove interference even when the frequency changes. We apply the method to the data produced by the Glasgow laser interferometer in 1996 and the entire series of wide lines corresponding to the electricity supply frequency and its harmonics are removed, leaving the spectrum clean enough to detect possible signals previously masked by them. We also study the effects of the line removal on the statistics of the noise in the time domain. We find that this technique seems to reduce the level of non-Gaussian noise present in the interferometer and therefore, it can raise the sensitivity and duty cycle of the detectors.Comment: 14 pages, 8 figures, Revtex, psfig. To appear in Phys. Rev.

Oversampling PCM techniques and optimum noise shapers for quantizing a class of nonbandlimited signals

We consider the efficient quantization of a class of nonbandlimited signals, namely, the class of discrete-time signals that can be recovered from their decimated version. The signals are modeled as the output of a single FIR interpolation filter (single band model) or, more generally, as the sum of the outputs of L FIR interpolation filters (multiband model). These nonbandlimited signals are oversampled, and it is therefore reasonable to expect that we can reap the same benefits of well-known efficient A/D techniques that apply only to bandlimited signals. We first show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of the signals. We can achieve a substantial decrease in bit rate by appropriately decimating the signals and then quantizing them. To further increase the effective quantizer resolution, noise shaping is introduced by optimizing prefilters and postfilters around the quantizer. We start with a scalar time-invariant quantizer and study two important cases of linear time invariant (LTI) filters, namely, the case where the postfilter is the inverse of the prefilter and the more general case where the postfilter is independent from the prefilter. Closed form expressions for the optimum filters and average minimum mean square error are derived in each case for both the single band and multiband models. The class of noise shaping filters and quantizers is then enlarged to include linear periodically time varying (LPTV)M filters and periodically time-varying quantizers of period M. We study two special cases in great detail

Gravitational wave radiometry: Mapping a stochastic gravitational wave background

The problem of the detection and mapping of a stochastic gravitational wave background (SGWB), either of cosmological or astrophysical origin, bears a strong semblance to the analysis of CMB anisotropy and polarization. The basic statistic we use is the cross-correlation between the data from a pair of detectors. In order to `point' the pair of detectors at different locations one must suitably delay the signal by the amount it takes for the gravitational waves (GW) to travel to both detectors corresponding to a source direction. Then the raw (observed) sky map of the SGWB is the signal convolved with a beam response function that varies with location in the sky. We first present a thorough analytic understanding of the structure of the beam response function using an analytic approach employing the stationary phase approximation. The true sky map is obtained by numerically deconvolving the beam function in the integral (convolution) equation. We adopt the maximum likelihood framework to estimate the true sky map that has been successfully used in the broadly similar, well-studied CMB map making problem. We numerically implement and demonstrate the method on simulated (unpolarized) SGWB for the radiometer consisting of the LIGO pair of detectors at Hanford and Livingston. We include `realistic' additive Gaussian noise in each data stream based on the LIGO-I noise power spectral density. The extension of the method to multiple baselines and polarized GWB is outlined. In the near future the network of GW detectors, including the Advanced LIGO and Virgo detectors that will be sensitive to sources within a thousand times larger spatial volume, could provide promising data sets for GW radiometry.Comment: 24 pages, 19 figures, pdflatex. Matched version published in Phys. Rev. D - minor change

Short-time homomorphic wavelet estimation

Successful wavelet estimation is an essential step for seismic methods like impedance inversion, analysis of amplitude variations with offset and full waveform inversion. Homomorphic deconvolution has long intrigued as a potentially elegant solution to the wavelet estimation problem. Yet a successful implementation has proven difficult. Associated disadvantages like phase unwrapping and restrictions of sparsity in the reflectivity function limit its application. We explore short-time homomorphic wavelet estimation as a combination of the classical homomorphic analysis and log-spectral averaging. The introduced method of log-spectral averaging using a short-term Fourier transform increases the number of sample points, thus reducing estimation variances. We apply the developed method on synthetic and real data examples and demonstrate good performance.Comment: 13 pages, 5 figures. 2012 J. Geophys. Eng. 9 67

A space communications study Final report, 15 Sep. 1966 - 15 Sep. 1967

Investigation of signal to noise ratios and signal transmission efficiency for space communication system

Optimum quantization of a class of non-bandlimited signals

We consider the quantization of a special class of non bandlimited signals, namely the class of discrete time signals that can be recovered from their decimated version. Similar to sigma-delta modulation ideas, we show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of these signals. We then consider noise shaping by optimizing a pre- and post filter around the quantizer and develop a closed form expression for the coding gain of the scheme under study. The use of an orthonormal filter bank as a sophisticated quantizer is investigated and several examples are provided

Light-emitting diodes and photodiodes in the deep ultra-violet range for absorption photometry in liquid chromatography, capillary electrophoresis and gas sensing

Absorbance measurement in the deep ultra-violet range (below 300 nm) has been one of the most widely used detection methods for analytical techniques as a large number of organic compounds have strong absorption bands in the deep UV region. The use of incandescent or discharge lamps coupled to a monochromator for the wavelength selection in a conventional UV detector makes it complex and costly. Light-emitting diodes (LEDs) for the deep UV range commercially available in recent years have become potential alternatives to thermal light sources. LEDs with their relatively narrow emission bandwidths (typically 20 nm) are well suited for absorption photometry in which a monochromator is not required. This dissertation, therefore, concerns the utilization LEDs and photodiodes (PDs) in the deep UV range as radiation sources and light detectors, respectively for absorption photometry in high-performance liquid chromatography (HPLC), capillary electrophoresis (CE) and gas sensing. LEDs were known to perform as light detectors. In measuring systems based on LEDs as light sources, PDs have been normally employed for detection devices. The practical reasons for the use of LEDs as alternatives to PDs, however, have not been demonstrated. Only an advantage of cost-saving was pointed out. In the first project, the performance of LEDs in the light intensity measurement was investigated and compared to that of standard silicon PDs in three different measuring configurations: current follower mode to measure to photocurrents, photovoltaic mode to determine the voltage developed across the diode on irradiation without load and discharge time mode to measure the rate to discharge the junction capacitance of diodes. LEDs as detectors were generally found to be adequate for the analytical work but PDs offered higher sensitivity and linearity as well as provided stable readings with faster settling times. Absorbance detectors for narrow-column HPLC (250 μm inner diameter) and CE (50 μm inner diameter) based on deep UV-LEDs and PDs selective for emission wavelengths were developed and evaluated in the quantification of model compounds at 255 and 280 nm. Absorbance measurements were directly obtained by the use of a beam splitter and PDs for reference signals and a logarithmic ratio amplifier-based circuitry to emulate the Lambert-Beer’s law. Narrow-column HPLC is useful for the applications in which the reduction in eluent consumption is desired or only limited amount of samples is available when utmost sensitivity is not required. In CE, the use of a capillary as the separation channel to minimize the peak broadening downscales the detection window to micrometer range which is even much narrower than that of a narrow-bore HPLC. This makes the design and construction of these LED-based detectors for narrow detection channels more challenging than for a standard HPLC as the higher efficiency for light coupling and stray light avoidance is essentially required. Additionally, high mechanical stability is needed to minimize the noise resulted from mechanical fluctuations. The performance of these optical devices at two measured wavelengths was excellent in terms of the baseline noise (low μAU range), linearity between absorbance values and concentrations (correlation coefficients > 0.999) and reproducibility of peak areas (about 1%). Not only was the potential of a deep UV-LED as a radiation source for absorption spectroscopy investigated for separation techniques but also for the detection of benzene, toluene, ethylbenzene and the xylenes compounds in the gas phase at 260 nm. In the first part of this work, its performance in the acoustic waves excitation was preliminarily investigated with some different measuring systems for the detection of the toluene vapor. It was found that the intensity of a deep UV-LED was insufficient to produce detectable acoustic signals. This was followed by the construction of an absorbance detector for the determination of these target compounds based on the combination of a deep UV-LED and PDs. This optical device was designed to use optical fibers for the light coupling from the LED to a measuring cell and a reference PD, that allows removing a beam splitter previously required for detectors of a narrow column HPLC and CE. Its performance with regard to linearity and reproducibility was satisfactory. Detection limits of about 1 ppm were determined. It could be concluded that viable absorbance detectors for narrow-column HPLC, CE and gas sensing based on deep UV-LEDs and PDs as light sources and light detectors, respectively can be constructed. The performance of these inexpensive LED-based optical devices with regard to linearity, reproducibility and baseline noise was satisfactory and found to be comparable to that of more complex and expensive commercial detectors. These detectors with features of low power consumption and small size are useful for portable battery-powered devices

Real-time filtering and detection of dynamics for compression of HDTV

The preprocessing of video sequences for data compressing is discussed. The end goal associated with this is a compression system for HDTV capable of transmitting perceptually lossless sequences at under one bit per pixel. Two subtopics were emphasized to prepare the video signal for more efficient coding: (1) nonlinear filtering to remove noise and shape the signal spectrum to take advantage of insensitivities of human viewers; and (2) segmentation of each frame into temporally dynamic/static regions for conditional frame replenishment. The latter technique operates best under the assumption that the sequence can be modelled as a superposition of active foreground and static background. The considerations were restricted to monochrome data, since it was expected to use the standard luminance/chrominance decomposition, which concentrates most of the bandwidth requirements in the luminance. Similar methods may be applied to the two chrominance signals

Energetic Quantum Limit in Large-Scale Interferometers

For each optical topology of an interferometric gravitational wave detector, quantum mechanics dictates a minimum optical power (the ``energetic quantum limit'') to achieve a given sensitivity. For standard topologies, when one seeks to beat the standard quantum limit by a substantial factor, the energetic quantum limit becomes impossibly large. Intracavity readout schemes may do so with manageable optical powers.Comment: Revised version; to be published in Proceedings of the 1999 Edoardo Amaldi Conference on Gravitational Waves; 11 pages including figures; manuscript is RevTex; figures are .eps; an AIP style file is include