Statistics, Probability and Noise

... 11CHAPTER 2Statistics, Probability and NoiseStatistics and probability are used in Digital Signal Processing to characterize signals and theprocesses that generate them. ... standard deviation and the peak-to-peak value of several commonwaveforms. Chapter 2- Statistics, Probability and Noise 15VppFVppFVppFVppFFIGURE 2-2Ratio of the peak-to-peak amplitude to the standard ....

Ngày tải lên: 13/09/2012, 09:49

... known that if the probability density function is standard nor- mal, that is f(x) = 1 √ 2π e − 1 2 x 2 , −∞ < x < ∞, then the mean µ = 0 and the standard deviation σ = 1, and the area between the ... saying the probability that a random variable is within k standard deviations of the mean is at least 1 − k −2 . Theorem 4.4 (Chebychev Inequality). Let X be a random variable with...

Ngày tải lên: 17/03/2014, 14:20

... heads and tails) and John 2 n ; jointly 2 2n+1 outcomes that are equally likely. Let H M and T M be the number of Mary’s heads and tails and H J and T J John’s, then H M + T M = n + 1 and H J + ... independent, (ii) A 2 and B are independent, and (iii) A 1 and A 2 are disjoint, then A 1 ∪A 2 and B are independent. If (i) and (ii) hold and A 1 ⊂A 2 then B and A 2 \A...

Ngày tải lên: 28/03/2014, 10:20

... statistics and graphical techniques may be used to sum- marize information about central tendency and/ or variability. 2.1 TABULAR AND GRAPHICAL PROCEDURES 2.1.1 Stem -and- leaf plot A stem -and- leaf ... (2.21) 2.2.13 Standard deviation The standard deviation is the positive square root of the variance: s = √ s 2 . The probable error is 0.6745 times the standard deviation. 2.2.14 Standa...

Ngày tải lên: 31/03/2014, 16:23

... INTRODUCTION 1 1.1 Organization of Text 2 1.2 Probability Tables and Computer Software 3 1.3 Prerequisites 3 PART A: PROBABILITY AND RANDOM VARIABLES 5 2 BASIC PROBABILITY CONCEPT S 7 2.1 Elements of ... 28 Problems 28 3 RANDOM VARIABLES A ND PROBABILITY DISTRIBUTIONS 37 3.1 Random Variables 37 3.2 Probability D istributions 39 3.2.1 Probability D istribution Function 39 3.2.2...

Ngày tải lên: 31/03/2014, 16:23

Ngày tải lên: 23/04/2014, 22:19

... non- Gaussian noise occurs often in practice. For instance, underwater acoustic noise, low-frequency atmospheric noise, radar clutter noise, and urban and man-made radio-frequency noise all are highly ... Model Validation, and Confidence Intervals Order Selection • Model Validation • Confidence Intervals 16.4 Noise Modeling Generalized Gaussian Noise • MiddletonClassANoise • St...

Ngày tải lên: 16/12/2013, 04:15

... 80 Hz; band 2 is band-pass and covers 80 Hz to 3 kHz; band 3 is high-pass and covers above 3 kHz; and band 4 is also high-pass and covers above 9 kHz. At the encoder the gain of each band is ... terms and in terms of probability functions. Bayesian inference theory provides a generalised framework for statistical processing of random signals, and for formulating and solvi...

Ngày tải lên: 21/01/2014, 07:20

... noise or any wideband noise whose spectrum has a non-flat shape; examples are pink noise, brown noise and autoregressive noise. (e) Impulsive noise: consists of short-duration pulses of random ... Estimation and Modulation Theory. Parts I, II and III. Wiley, New York. 2 NOISE AND DISTORTION 2.1 Introduction 2.6 Thermal Noise 2.2 White Noise 2.7 Shot...

Ngày tải lên: 21/01/2014, 07:20

... Autocorrelation and power spectrum of impulsive noise. Impulsive noise is a random, binary-state (“on/off”) sequence of impulses of random amplitudes and random time of occurrence. In Chapter 12, a random ... impulse, and n(m) is a random noise process. Assuming P XX (f) f r xx (m) m Figure 3.6 Autocorrelation and power spectrum of white noise. 62 Probability Models...

Ngày tải lên: 21/01/2014, 07:20