White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.

Speech bandwidth extension method and apparatus

Abstract: A speech bandwidth extension method and apparatus analyzes narrowband speech sampled at 8 kHz using LPC analysis to determine its spectral shape and inverse filtering to extract its excitation signal. The excitation signal is interpolated to a sampling rate of 16 kHz and analyzed for pitch control and power level. A white noise generated wideband signal is then filtered to provide a synthesized wideband excitation signal. The narrowband shape is determined and compared to templates in respective vector quantizer codebooks, to select respective highband shape and gain. The synthesized wideband excitation signal is then filtered to provide a highband signal which is, in turn, added to the narrowband signal, interpolated to the 16 kHz sample rate, to produce an artificial wideband signal. The apparatus may be implemented on a digital signal processor chip.

Initial results in electromechanical mode identification from ambient data

Abstract: Power system loads are constantly changing. Over a time-span of a few minutes, these changes are primarily random. The random load variations act as a constant low-level excitation to the electromechanical dynamics of the power system which shows up as ambient noise in field measured voltage, current and power signals. Assuming the random variations are white and stationary over an analysis window, it is theoretically possible to estimate the electromechanical modal frequencies and damping from the spectral content of the ambient noise. In this paper, field collected ambient noise is analyzed by solving the Wiener-Hopf linear prediction equations to estimate the modal frequency and damping. These estimates are then compared with results from a Prony analysis on a ringdown resulting from a 1400 MW brake insertion under the same operating conditions as the ambient data. Results show that estimates are consistent between the ambient and ringdown analysis indicating that it is possible to estimate a power system's electromechanical characteristics simply from ambient data. These results demonstrate that it may be possible to provide power system control and operation algorithms with a real-time estimate of modal frequency and damping.

Correlated errors in geodetic time series: Implications for time‐dependent deformation

Abstract: Analysis of frequent trilateration observations from the two-color electronic distance measuring networks in California demonstrate that the noise power spectra are dominated by white noise at higher frequencies and power law behavior at lower frequencies. In contrast, Earth scientists typically have assumed that only white noise is present in a geodetic time series, since a combination of infrequent measurements and low precision usually preclude identifying the time-correlated signature in such data. After removing a linear trend from the two-color data, it becomes evident that there are primarily two recognizable types of time-correlated noise present in the residuals. The first type is a seasonal variation in displacement which is probably a result of measuring to shallow surface monuments installed in clayey soil which responds to seasonally occurring rainfall; this noise is significant only for a small fraction of the sites analyzed. The second type of correlated noise becomes evident only after spectral analysis of line length changes and shows a functional relation at long periods between power and frequency of 1/ƒα, where ƒ is frequency and α≈2. With α=2, this type of correlated noise is termed random-walk noise, and its source is mainly thought to be small random motions of geodetic monuments with respect to the Earth's crust, though other sources are possible. Because the line length changes in the two-color networks are measured at irregular intervals, power spectral techniques cannot reliably estimate the level of 1/ƒα noise. Rather, we also use here a maximum likelihood estimation technique which assumes that there are only two sources of noise in the residual time series (white noise and random-walk noise) and estimates the amount of each. From this analysis we find that the random-walk noise level averages about 1.3 mm/√yr and that our estimates of the white noise component confirm theoretical limitations of the measurement technique. In addition, the seasonal noise can be as large as 3 mm in amplitude but typically is less than 0.5 mm. Because of the presence of random-walk noise in these time series, modeling and interpretation of the geodetic data must account for this source of error. By way of example we show that estimating the time-varying strain tensor (a form of spatial averaging) from geodetic data having both random-walk and white noise error components results in seemingly significant variations in the rate of strain accumulation; spatial averaging does reduce the size of both noise components but not their relative influence on the resulting strain accumulation model.

The Noise-Sensitivity Phase Transition in Compressed Sensing

Abstract: Consider the noisy underdetermined system of linear equations: y = Ax0 + z, with A an n × N measurement matrix, n <; N, and z ~ N(0, σ2I) a Gaussian white noise. Both y and A are known, both x0 and z are unknown, and we seek an approximation to x0. When x0 has few nonzeros, useful approximations are often obtained by l1-penalized l2 minimization, in which the reconstruction x1,λ solves min{||y - Ax||22/2 + λ||x||1}. Consider the reconstruction mean-squared error MSE = E|| x1,λ - x0||22/N, and define the ratio MSE/σ2 as the noise sensitivity. Consider matrices A with i.i.d. Gaussian entries and a large-system limit in which n, N → ∞ with n/N → δ and k/n → ρ. We develop exact expressions for the asymptotic MSE of x1,λ , and evaluate its worst-case noise sensitivity over all types of k-sparse signals. The phase space 0 ≤ 8, ρ ≤ 1 is partitioned by the curve ρ = ρMSE(δ) into two regions. Formal noise sensitivity is bounded throughout the region ρ = ρMSE(δ) and is unbounded throughout the region ρ = ρMSE(δ). The phase boundary ρ = ρMSE(δ) is identical to the previously known phase transition curve for equivalence of l1 - l0 minimization in the k-sparse noiseless case. Hence, a single phase boundary describes the fundamental phase transitions both for the noise less and noisy cases. Extensive computational experiments validate these predictions, including the existence of game-theoretical structures underlying it (saddlepoints in the payoff, least-favorable signals and maximin penalization). Underlying our formalism is an approximate message passing soft thresholding algorithm (AMP) introduced earlier by the authors. Other papers by the authors detail expressions for the formal MSE of AMP and its close connection to l1-penalized reconstruction. The focus of the present paper is on computing the minimax formal MSE within the class of sparse signals x0.