Stochastic signals

It is impossible to predict the amplitude of a stochastic signal at a certain time in the future in contrast to a deterministic signal like a sine wave. Only a statistical description, for instance by distribution functions and autocorrelation functions, can be given. Host kinds of noise have a stochastic character. 

An ACF is always an even function, symmetrical with respect to =0. The fast decreasing ACF of a very fast fluctuating stochastic signal can be considered as an impulse. 

In the case of pulverized coal flow measurement, the concentration of the pulverized coal is measured by low-power, low-frequency microwave sensors. The variation in the microwave transmission characteristic (dielectric load) is caused by the changing coal concentration, which produces shifts in measurement frequency. The resulting quantifiable values indicate the coal density. This concentration measurement is performed by a microwave transmitter and a microwave receiver, as shown in Figure 3.90. The velocity of the pulverized coal is measured by two identical microwave devices by crosscorrelation. Here, the pair of sensors detect the stochastic signals resulting from the charged coal particles, which are nearly identical but shifted by the time the pulverized coal gets from one sensor to the other. 

T Blaffert (1995) Theory of stochastic signal processing for the optimization of explosives detection. SPIE 2511, 108-119. 

An important feature of a process signal is its periodicity, or, in other words, its frequency content. Fourier theory indicates that it is possible to separate individual frequency components from stationary signals (i.e., stochastic signals whose statistical characteristics do not change over time) and make a transformation from the amplitude-time domain to the amplitude-frequency domain. This transformation is known as the Fourier Transform (FT). The Fourier transform of a continuous stationary signal z t) for a given frequency to in radians is defined as. 

Pan, Y. X., Z. Z. Zhang, Z. M. Guo, G. Y. Feng, Z. D. Huang, and L. He. 2003. Application of pseudo amino acid composition for predicting protein subcellular location Stochastic signal processing approach. J Protein Chem 22 395-402. 

Superior efficacy of periodic versus chaotic or stochastic signalling in intercellular communication... 

Miyanaga, Y., Matsuoka, S., Yanagida, T., and Ueda, M. (2007) Stochastic signal inputs for chemotactic response in Dictyostdium cells revealed by single molecule imaging techniques. Biosystems 88, 251-260. 

Ueda, M. and Shibata, T. (2007) Stochastic signal processing and transduction in chemotactic response of eukaryotic cells. Biophys. J. 93, 11-20. 

The digital results, in particular, may be easily extended in a number of directions. Stochastic signals, rather than sinewave signals, could be treated in the binary communication problem. An extensive treatment of M-ary communications is possible, as is the generalization from a single detector to an array of detectors [7.76-78]. Consideration could be given to the optimum matched filter detector rather than the envelope detector discussed earlier. While the present treatment consists of a per-symbol analysis, prediction could be used to estimate the atmospheric turbulence level over a time period from a particular symbol, for example. In short, the usual variations possible with the conventional heterodyne system may be extended and/or modified for application to the three-frequency nonlinear heterodyne technique. 

The following sections arc organized as follows. Section 18.3 deals with an ysis of deterministic and stationary stochastic signals. Analysis of nonstationary signals is discussed in Sec. 18.4. Sub-... 

In general, parametric mediods are preferred for stochastic signals, provided the estimations of model order and the model parameters are done carefiilly. 

Estimating time delay or propagation delay between two biosignals (deterministic or stochastic signals in noise)... 

---