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Bandpass Random Process

Lecture 16EEE 352 Analog Communication Systems

Mansoor KhanElectrical Engineering Dept.CIIT Islamabad Campus

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Noise

Noise refers to unwanted interference that tends toobscure the information bearing signal

Noise can be classified into two categories:

Man-made Noise introduced by switching transients and simultaneouspresence of neighboring signals

Natural Noise produced by the atmosphere and heating up of electricalcomponents. The latter is referred to as the Thermal noise

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Thermal noise is difficult to be eliminated and often modeled by theGaussian probability density function

Additive Gaussian Noise: refers to the following model forintroduction of noise in the signal

Given that the noise n is a Gaussian RV and a is the dc component,which is constant, the pdf of z is given by

Additive Gaussian Noise

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Additive Gaussian NoiseDistribution

The normalized or standardized Gaussian density function of a zero-mean process is obtained byassuming unit variance.

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Additive White Gaussian Noise The primary spectral characteristic of thermal noise is that its power

spectral density is the same for all frequencies of interest in mostcommunication systems

Power spectral density S n (w )

Autocorrelation function of white noise is

The average power P n of white noise is infinite

2

N wSn

21 N wSF R nn

df N

Pn 2

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Bandpass Random Processes

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Bandpass Random Processes (cont)

Consider the system response to an input t

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Bandpass Random Processes (cont)

dsada

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Bandpass Random Processes (cont)

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Bandpass Random Processes (cont)

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Example

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Example (cont)

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Problem 11.1-7

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