analog communicationLecture 16

Bandpass Random Process

Lecture 16 EEE 352 Analog Communication Systems Mansoor Khan Electrical Engineering Dept. CIIT Islamabad Campus

Noise • Noise refers to unwanted interference that tends to obscure the information bearing signal • Noise can be classified into two categories: – Man-made Noise introduced by switching transients and simultaneous presence of neighboring signals

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

Additive Gaussian Noise •

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

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

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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 Distribution • The normalized or standardized Gaussian density function of a zero-mean process is obtained by assuming unit variance.

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 most communication systems • Power spectral density Sn(w )

N S n w  2 • Autocorrelation function of white noise is

N Rn    F S n w     2 1

• The average power Pn of white noise is infinite 

N Pn   df   2 

Bandpass Random Processes

Bandpass Random Processes (cont) • Consider the system response to an input  t   

Bandpass Random Processes (cont) • dsada

Bandpass Random Processes (cont)

Bandpass Random Processes (cont)

Example

Example (cont)

Problem 11.1-7