S. Mandayam/ ECOMMS/ECE Dept./Rowan University Electrical Communications Systems Spring 2005 Shreekanth Mandayam ECE Department Rowan University Lecture 1b January 19, 2005

S. Mandayam/ ECOMMS/ECE Dept./Rowan University ECOMMS: Topics

S. Mandayam/ ECOMMS/ECE Dept./Rowan University ECOMMS: Topics

S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityPlan Baseband and Bandpass Signals Recall: Comm. Sys. Block diagram Aside: Why go to higher frequencies? International & US Frequency Allocations Intoduction to Information Theory Recall: List of topics Probability Information Entropy Signals and Noise

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Comm. Sys. Bock Diagram Tx s(t) Channel r(t) m(t) Noise Rx Baseband Signal Baseband Signal Bandpass Signal “Low” Frequencies <20 kHz Original data rate “High” Frequencies >300 kHz Transmission data rate Modulation Demodulation or Detection Formal definitions will be provided later

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Aside: Why go to higher frequencies? Tx /2 Half-wave dipole antenna c = f c = 3E+08 ms -1 Calculate for f = 5 kHz f = 300 kHz There are also other reasons for going from baseband to bandpass

S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityInformation Info Source Info Source Info Sink Info Sink Comm System Recall: Information Source: a system that produces messages (waveforms or signals) Digital/Discrete Information Source: Produces a finite set of possible messages Digital/Discrete Waveform: A function of time that can only have discrete values Digital Communication System: Transfers information from a digital source to a digital sink

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Another Classification of Signals (Waveforms) Deterministic Signals: Can be modeled as a completely specified function of time Random or Stochastic Signals: Cannot be completely specified as a function of time; must be modeled probabilistically What type of signals are information bearing?

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Signals and Noise Strictly, both signals and noise are stochastic and must be modeled as such We will make these approximations, initially: Noise is ignored Signals are deterministic Comm. Waveform Signal (desired) Noise (undesired) Lab 1

S. Mandayam/ ECOMMS/ECE Dept./Rowan University Measures of Information Definitions Probability Information Entropy Source Rate Recall: Shannon’s Theorem If R < C = B log 2 (1 + S/N), then we can have error- free transmission in the presence of noise MATLAB DEMO: entropy.m

S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversitySummary