Noise is additional\unwanted \signal that interferes with the transmitted signal Generated by electronic devices The noise is a random process Each\sample \ of n(tis a random variable Typically, the noise process is modeled as\Additive White Gaussian noise”(AWGN) White: Flat frequency spectrur Gaussian noise distribution

Channel Coding When transmitting over a noisy channel, some of the bits are received with errors Example: Binary Symmetric Channel (BSc) Pe= probability oferror Q: How can these errors be removed? A: Coding: the addition of redundant bits that help us determine what was sent with greater accuracy

The signal suffers an attenuation loss l Received power PR= PT/L Received snr=E,/No, Eb=Pr/Rb Antennas are used to compensate for attenuation loss Capture as much of the signal as possible

Source coding Source Encode Channel Alphabet alphabet Source symbols Letters of alphabet, ASClI symbols, English

Sampling Sampling provides a discrete-time representation of a continuous waveform Sample points are real-valued numbers In order to transmit over a digital system we must first convert into discrete valued numbers

Sampling Given a continuous time waveform, can we represent it using discrete samples? How often should we sample? Can we reproduce the original waveform?

Information content of a random variable Random variable x Outcome of a random experiment Discrete R V takes on values from a finite set of possible outcomes PMF: P(X=y)=Py) How much information is contained in the event X=y? Will the sun rise today Revealing the outcome of this experiment provides no information Will the Celtics win the NBa championship? Since this is unlikely, revealing yes provides more information than revealing Events that are less likely contain more information than likely events

Administrative matters Instructors: Eytan Modiano Meeting times: Tuesdays and Thursdays Text: Communications Systems engineering Proakis and salehi Grading 10% weekly Homework Assignments 30% each of 3 exams Final exam during final exam period

Final exam Very good performance overall Essays were particularly good ·Mean-88.5%0 Standard deviation -5.7%

The mahalanobis distance in Character Recognition Authored by Dan Frey 31 July 98 This sheet explores the use of the Mahalanobis Distance in character It defines a letters a.b.c. and d It creates a population of distorted letters to train a classifier