Topic

# White noise

About: White noise is a(n) research topic. Over the lifetime, 16496 publication(s) have been published within this topic receiving 318633 citation(s).

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Bell Labs

^{1}TL;DR: A method is developed for representing any communication system geometrically and a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect.

Abstract: A method is developed for representing any communication system geometrically Messages and the corresponding signals are points in two "function spaces," and the modulation process is a mapping of one space into the other Using this representation, a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect Formulas are found for the maximum rate of transmission of binary digits over a system when the signal is perturbed by various types of noise Some of the properties of "ideal" systems which transmit at this maximum rate are discussed The equivalent number of binary digits per second for certain information sources is calculated

6,364 citations

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TL;DR: The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF.

Abstract: A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This new approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a time–space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturall...

5,108 citations

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TL;DR: Generation and estimation of these models are considered and applications on generated and real data presented, showing potentially useful long-memory forecasting properties.

Abstract: . The idea of fractional differencing is introduced in terms of the infinite filter that corresponds to the expansion of (1-B)d. When the filter is applied to white noise, a class of time series is generated with distinctive properties, particularly in the very low frequencies and provides potentially useful long-memory forecasting properties. Such models are shown to possibly arise from aggregation of independent components. Generation and estimation of these models are considered and applications on generated and real data presented.

3,098 citations

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TL;DR: In this paper, it is shown that the residual autocorrelations are to a close approximation representable as a singular linear transformation of the auto-correlations of the errors so that they possess a singular normal distribution.

Abstract: Many statistical models, and in particular autoregressive-moving average time series models, can be regarded as means of transforming the data to white noise, that is, to an uncorrelated sequence of errors. If the parameters are known exactly, this random sequence can be computed directly from the observations; when this calculation is made with estimates substituted for the true parameter values, the resulting sequence is referred to as the "residuals," which can be regarded as estimates of the errors. If the appropriate model has been chosen, there will be zero autocorrelation in the errors. In checking adequacy of fit it is therefore logical to study the sample autocorrelation function of the residuals. For large samples the residuals from a correctly fitted model resemble very closely the true errors of the process; however, care is needed in interpreting the serial correlations of the residuals. It is shown here that the residual autocorrelations are to a close approximation representable as a singular linear transformation of the autocorrelations of the errors so that they possess a singular normal distribution. Failing to allow for this results in a tendency to overlook evidence of lack of fit. Tests of fit and diagnostic checks are devised which take these facts into account.

2,296 citations

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TL;DR: A new optical encoding method of images for security applications is proposed and it is shown that the encoding converts the input signal to stationary white noise and that the reconstruction method is robust.

Abstract: We propose a new optical encoding method of images for security applications. The encoded image is obtained by random-phase encoding in both the input and the Fourier planes. We analyze the statistical properties of this technique and show that the encoding converts the input signal to stationary white noise and that the reconstruction method is robust.

2,163 citations