The effect of signal digitisation in CMB experiments

Signal digitisation may produce significant effects in balloon - borne or space CMB experiments, since the limited bandwidth for downlink of data requires imposes a large quantisation step q applied on board by the instrument acquisition chain. In this paper we present a study of the impact of the quantization error in CMB experiments using, as a working case, simulated data from the Planck/LFI. At TOD level, the effect of the quantization can be approximated as a source of nearly normally distributed noise. At map level, the data quantization alters the noise distribution and the expectation of some higher order moments. Finally, at the levell of power spectra, the quantization introduces a power excess, that, although related to the instrument and mission parameters, is weakly dependent on the multipole l at middle and large l and can be quite accurately subtracted, leaving a residual uncertainty of few % of the RMS uncertainty. Only for l<30 the quantization removal is less accurate.Comment: 15 pages, 5 figures, LaTeX2e, A&A style (aa.cls). Release 1, april 1st 2003. Submitted to A&A for the pubblication, april 1st 2003. Contact author: [email protected]

Peak harmonic distortion due to quantization

In this thesis, the problem of quantization noise 1s presented, and recent efforts 1n this area are reviewed. With the motivation for further Investigation Into the problem explained, the purpose of this thesis 1s stated to be the determination of peak harmonic distortion due to quantization for predominantly single frequency Inputs. Two cases were examined with pure sinusoid and sine wave plus Gaussian bandlimited white noise. The method used was to simulate the quantization process on the computer, and to use a Fast Fourier Transform algorithm to analyze the spectra of the quantized signals. For pure sinusoidal Inputs, the location of the peak harmonic distortion 1n the quantization noise spectrum was found to be very sensitive to the degree of loading of the quantizer. However the magnitude of the peak distortion when plotted as a function of the number of bits totally used by the Input was fitted very well with a straight line of slope -6dB/b1t. Moreover the largest component 1n the quantization noise spectrum was observed to be about 4dB above the average noise spectral density across the entire frequency band of observation. The addition of noise to the sine wave was anticipated to have a smoothing effect on the quantization noise spectrum. This phenomenon was observed for a specific set of Input noise samples but the results are not conclusive, becuase after further investigation of the noise generation mechanism, the statistical properties of the synthesized noise signal were found to be unsuitable for analysis of power spectra. However since the pure sinusoidal inputs represent the worst case condition for harmonic distortion due to quantization, the measured peaks will provide the upper bounds necessary for specifications in engineering system designs

Digital test signal generation: An accurate SNR calibration approach for the DSN

A new method of generating analog test signals with accurate signal to noise ratios (SNRs) is described. High accuracy will be obtained by simultaneous generation of digital noise and signal spectra at a given baseband or bandpass limited bandwidth. The digital synthesis will provide a test signal embedded in noise with the statistical properties of a stationary random process. Accuracy will only be dependent on test integration time with a limit imposed by the system quantization noise (expected to be 0.02 dB). Setability will be approximately 0.1 dB. The first digital SNR generator to provide baseband test signals is being built and will be available in early 1991

Digital Color Imaging

This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented us-ing vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided

Circular polarization measurement in millimeter-wavelength spectral-line VLBI observations

This paper considers the problem of accurate measurement of circular polarization in imaging spectral-line VLBI observations in the lambda=7 mm and lambda=3 mm wavelength bands. This capability is especially valuable for the full observational study of compact, polarized SiO maser components in the near-circumstellar environment of late-type, evolved stars. Circular VLBI polarimetry provides important constraints on SiO maser astrophysics, including the theory of polarized maser emission transport, and on the strength and distribution of the stellar magnetic field and its dynamical role in this critical circumstellar region. We perform an analysis here of the data model containing the instrumental factors that limit the accuracy of circular polarization measurements in such observations, and present a corresponding data reduction algorithm for their correction. The algorithm is an enhancement of existing spectral line VLBI polarimetry methods using autocorrelation data for calibration, but with innovations in bandpass determination, autocorrelation polarization self-calibration, and general optimizations for the case of low SNR, as applicable at these wavelengths. We present an example data reduction at $\lambda=7$ mm and derive an estimate of the predicted accuracy of the method of m_c < 0.5% or better at lambda=7 mm and m_c < 0.5-1% or better at lambda=3 mm. Both the strengths and weaknesses of the proposed algorithm are discussed, along with suggestions for future work.Comment: 23 pages, 13 figure

Components for oversampled signal processors

Oversampled converters trade transmission bandwidth for resolution. An idealized model gives an insight into the way in which signals are encoded and thus how they can be manipulated. Oversampling offers a form of signal processing that requires simple processing elements capable of exploiting the growing clock speeds available in integrated solutions. Simultaneously avoids the need for analog circuitry. This paper reviews common operations that can be performed on oversampled signals

Analysis of VCO based noise shaping ADCs linearized by PWM modulation

Nonlinearity is one of the main problems associated with VCO based noise shaping ADCs. Their open loop architecture does not permit correction of the nonlinear voltage to frequency response of the VCO by feedback. Recently, linearization of a VCO ADC by Pulse Width Modulation (PWM) precoding has been proposed. Here, the input signal is encoded by a PWM modulator to drive the VCO with a 2-level signal, thus eliminating the nonlinearity of the VCO. This paper analyzes the remaining inherent distortion in such modulators which originates from subsampling the PWM sidebands

Colored-Gaussian Multiple Descriptions: Spectral and Time-Domain Forms

It is well known that Shannon's rate-distortion function (RDF) in the colored quadratic Gaussian (QG) case can be parametrized via a single Lagrangian variable (the "water level" in the reverse water filling solution). In this work, we show that the symmetric colored QG multiple-description (MD) RDF in the case of two descriptions can be parametrized in the spectral domain via two Lagrangian variables, which control the trade-off between the side distortion, the central distortion, and the coding rate. This spectral-domain analysis is complemented by a time-domain scheme-design approach: we show that the symmetric colored QG MD RDF can be achieved by combining ideas of delta-sigma modulation and differential pulse-code modulation. Specifically, two source prediction loops, one for each description, are embedded within a common noise shaping loop, whose parameters are explicitly found from the spectral-domain characterization.Comment: Accepted for publications in the IEEE Transactions on Information Theory. Title have been shortened, abstract clarified, and paper significantly restructure

Numerical investigation of the quantum fluctuations of optical fields transmitted through an atomic medium

We have numerically solved the Heisenberg-Langevin equations describing the propagation of quantized fields through an optically thick sample of atoms. Two orthogonal polarization components are considered for the field and the complete Zeeman sublevel structure of the atomic transition is taken into account. Quantum fluctuations of atomic operators are included through appropriate Langevin forces. We have considered an incident field in a linearly polarized coherent state (driving field) and vacuum in the perpendicular polarization and calculated the noise spectra of the amplitude and phase quadratures of the output field for two orthogonal polarizations. We analyze different configurations depending on the total angular momentum of the ground and excited atomic states. We examine the generation of squeezing for the driving field polarization component and vacuum squeezing of the orthogonal polarization. Entanglement of orthogonally polarized modes is predicted. Noise spectral features specific of (Zeeman) multi-level configurations are identified.Comment: 12 pages 9 figures. Submitted to Physical Review