J.M. Mendel, Tutorial on higher-order statistics(spectra) in signal processing and systems theory: Theoretical results and some applications, " Proc. IEEE, vol. 79, Pp. 278-305, 1991 H V. Poor, An Introduction to Signal Detection and Estimation, 2nd ed, New York: Springer-Verlag, 1994 H V Poor and J B. Thomas,Signal detection in dependent non-Gaussian noise, "in Advances in Statistical Signal br. p Processing, vol 2, Signal Detection, H V. Poor and J.B. Thomas, Eds, Greenwich, Conn: JAI Press, 1993 J.G. Proakis, Digital Communications, New York: McGraw-Hill, 1983 DL. Snyder and M.I. Miller, Random Point Processes in Time and Space, New York: Springer-Verlag, 1991 J. Tsitsiklis, Distributed detection, "in Advances in Statistical Signal Processing, vol. 2, Signal Detection, H V. Poor and J B. Thomas, Eds, Greenwich, Conn. JAI Press, 1993 S. Verdu, Multiuser detection, " in Advances in Statistical Signal Processing, vol 2, Signal Detection, H V. Poor and J B. Thomas, Eds, Greenwich, Conn. JAI Press, 1993 Further Information Except as otherwise noted in the accompanying text, further details on the topics introduced in this section can be found in the textbook. Poor, H.V. An Introduction to Signal Detection and Estimation, 2nd ed, New York: Springer-Verlag, 1994 The bimonthly journal, IEEE Transactions on Information Theory publishes recent advances in the theory of signal detection. It is available from the Institute of Electrical and Electronics Engineers, Inc, 345 East 47th Street, New York, NY 10017 Papers describing applications of signal detection are published in a number of journals, including the monthly journals IEEE Transactions on Communications, IEEE Transactions on Signal Processing, and the Journal of the Acoustical Society of America. The IEEE journals are available from the IEEE, as above. The Journal of the Acoustical Society of America is available from the American Institute of Physics, 335 East 45th Street, New York, NY10017 73.2 Noise Carl G. Looney Every information signal s( t) is corrupted to some extent by the superimposition of extra-signal fluctuations that assume unpredictable values at each time instant t. Such undesirable signals were called noise due to early measurements with sensitive audio amplifiers Noise sources are(1)intrinsic,(2)external, or(3)process induced Intrinsic noise in conductors comes from thermal agitation of molecularly bound ions and electrons, from microboundaries of impurities and grains with varying potential, and from transistor junction areas that become temporarily depleted of electrons/holes. External electromagnetic interference sources include airport radar, x-rays, power and telephone lines, com munications transmissions, gasoline engines and electric motors, computers and other electronic devices; and also include lightning, cosmic rays, plasmas(charged particles)in space, and solar/stellar radiation(conductors act as antennas). Reflective objects and other macroboundaries cause multiple paths of signals. Process-induced errors include measurement, quantization, truncation, and signal generation errors. These also corrupt the ignal with noise power and loss of resolution Statistics of noise Statistics allow us to analyze the spectra of noise. We model a noise signal by a random(or stochastic) process N(o, a function whose realized value N(n)=x, at any time instant t is chosen by the outcome of the random variable N,=N(o). N(o) has a probability distribution for the values x it can assume Any particular trajectory , x ) of outcomes is called a realization of the noise process. The first-order statistic of N(o)is the expected value u, EIN(D]. The second-order statistic is the autocorrelation function RN(t, t+ t)=EINON(t+ t)l, N,=N(t)and N2=N(t2) at times ti and t2 depend on each other in an average sense oise random variables where E[-] is the expected value operator Autocorrelation measures the extent to which no e 2000 by CRC Press LLC© 2000 by CRC Press LLC J.M. Mendel, “Tutorial on higher-order statistics (spectra) in signal processing and systems theory: Theoretical results and some applications,’’ Proc. IEEE, vol. 79, pp. 278–305, 1991. H.V. Poor, An Introduction to Signal Detection and Estimation, 2nd ed., New York: Springer-Verlag, 1994. H.V. Poor and J. B. Thomas, “Signal detection in dependent non-Gaussian noise,’’ in Advances in Statistical Signal Processing, vol. 2, Signal Detection, H.V. Poor and J.B. Thomas, Eds., Greenwich, Conn.: JAI Press, 1993. J.G. Proakis, Digital Communications, New York: McGraw-Hill, 1983. D.L. Snyder and M.I. Miller, Random Point Processes in Time and Space, New York: Springer-Verlag, 1991. J. Tsitsiklis, “Distributed detection,’’ in Advances in Statistical Signal Processing, vol. 2, Signal Detection, H.V. Poor and J.B. Thomas, Eds., Greenwich, Conn.: JAI Press, 1993. S. Verdú, “Multiuser detection,’’ in Advances in Statistical Signal Processing, vol. 2, Signal Detection, H.V. Poor and J.B. Thomas, Eds., Greenwich, Conn.: JAI Press, 1993. Further Information Except as otherwise noted in the accompanying text, further details on the topics introduced in this section can be found in the textbook: Poor, H.V. An Introduction to Signal Detection and Estimation, 2nd ed., New York: Springer-Verlag, 1994. The bimonthly journal, IEEE Transactions on Information Theory, publishes recent advances in the theory of signal detection. It is available from the Institute of Electrical and Electronics Engineers, Inc., 345 East 47th Street, New York, NY 10017. Papers describing applications of signal detection are published in a number of journals, including the monthly journals IEEE Transactions on Communications, IEEE Transactions on Signal Processing, and the Journal of the Acoustical Society of America. The IEEE journals are available from the IEEE, as above. The Journal of the Acoustical Society of America is available from the American Institute of Physics, 335 East 45th Street, New York, NY 10017. 73.2 Noise Carl G. Looney Every information signal s(t) is corrupted to some extent by the superimposition of extra-signal fluctuations that assume unpredictable values at each time instant t. Such undesirable signals were called noise due to early measurements with sensitive audio amplifiers. Noise sources are (1) intrinsic, (2) external, or (3) process induced. Intrinsic noise in conductors comes from thermal agitation of molecularly bound ions and electrons, from microboundaries of impurities and grains with varying potential, and from transistor junction areas that become temporarily depleted of electrons/holes. External electromagnetic interference sources include airport radar, x-rays, power and telephone lines, com￾munications transmissions, gasoline engines and electric motors, computers and other electronic devices; and also include lightning, cosmic rays, plasmas (charged particles) in space, and solar/stellar radiation (conductors act as antennas). Reflective objects and other macroboundaries cause multiple paths of signals. Process-induced errors include measurement, quantization, truncation, and signal generation errors. These also corrupt the signal with noise power and loss of resolution. Statistics of Noise Statistics allow us to analyze the spectra of noise. We model a noise signal by a random (or stochastic) process N(t), a function whose realized value N(t) = xt at any time instant t is chosen by the outcome of the random variable Nt = N(t). N(t) has a probability distribution for the values x it can assume. Any particular trajectory {(t,xt)} of outcomes is called a realization of the noise process. The first-order statistic of N(t) is the expected value mt = E[N(t)]. The second-order statistic is the autocorrelation function RNN(t, t + t) = E[N(t)N(t + t)], where E[–] is the expected value operator.Autocorrelation measures the extent to which noise random variables N1 = N(t1) and N2 = N(t2 ) at times t1 and t2 depend on each other in an average sense