By Wim C. Van Etten
Random indications and noise are found in many engineering platforms and networks. sign processing options permit engineers to differentiate among worthy signs in audio, video or verbal exchange gear, and interference, which disturbs the specified signal.With a robust mathematical grounding, this article offers a transparent advent to the basics of stochastic procedures and their useful purposes to random signs and noise. With labored examples, difficulties, and precise appendices, creation to Random indications and Noise supplies the reader the information to layout optimal platforms for successfully dealing with undesirable signals.Key features:Considers a variety of indications and noise, together with analogue, discrete-time and bandpass signs in either time and frequency domains.Analyses the fundamentals of electronic sign detection utilizing matched filtering, sign house illustration and correlation receiver.Examines optimum filtering equipment and their consequences.Presents a close dialogue of the subject of Poisson approaches and shot noise.An first-class source for pro engineers constructing conversation structures, semiconductor units, and audio and video apparatus, this publication is additionally perfect for senior undergraduate and graduate scholars in digital and electric Engineering.
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Extra info for Introduction to Random Signals and Noise
To answer this we determine both the ensemble mean and the time average. 1 2T ! t À Þ d ¼ 0 ð2:27Þ 0 Hence, time and ensemble averages are equal. Let us now calculate the two autocorrelation functions. 1 2T 2 ÀT A½XðtÞ Xðt þ Þ ¼ lim ð2:28Þ The ﬁrst term of the latter integral equals 0. The second term of the integrand does not depend on the integration variable. Þ d ¼ 2p 2 0 E½XðtÞ Xðt þ Þ ¼ ð2:30Þ 16 STOCHASTIC PROCESSES Of the latter integral the ﬁrst part is 0. Again, the second term of the integrand does not depend on the integration variable.
Secondly, the relative height of the peak can be interpreted as a measure for the size of the object. It will be clear that this method is very useful in such ranging systems as radar and underwater acoustic distance measurement. Most ranging systems use pulsed continuous wave (CW) signals for that. The advantage of the system presented here is the fact that for the transmitted signal a noise waveform is used. Such a waveform cannot easily be detected by the probed object, in contrast to the pulsed CW systems, since it has no replica available of the transmitted signal and therefore is not able to perform the correlation.
A) Are the processes XðtÞ and YðtÞ wide-sense stationary? (b) Are they jointly wide-sense stationary? 0 constants, and Â a random variable that is uniformly distributed on the interval ð0; 2p. We deﬁne a new process by means of YðtÞ ¼ X 2 ðtÞ. (a) (b) (c) (d) (e) (f) Are XðtÞ and YðtÞ wide-sense stationary? Calculate the autocorrelation function of YðtÞ. Calculate the cross-correlation function of XðtÞ and YðtÞ. Are XðtÞ and YðtÞ jointly wide-sense stationary? Calculate and sketch the probability distribution function of YðtÞ.