1 / 9

Lecture 3 Outline

Lecture 3 Outline. Announcements: No class Wednesday Friday lecture (1/17) start at 12:50pm Review of Last Lecture Communication System Block Diagram Performance Metrics Fundamental Rate Limits and Shannon Capacity Periodic Signals and Fourier Series. Review of Last Lecture.

todd
Download Presentation

Lecture 3 Outline

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 3 Outline • Announcements: • No class Wednesday • Friday lecture (1/17) start at 12:50pm • Review of Last Lecture • Communication System Block Diagram • Performance Metrics • Fundamental Rate Limits and Shannon Capacity • Periodic Signals and Fourier Series

  2. Review of Last Lecture • Analog, digital, and binary signals • Analog communication systems • Convert analog information signals to modulated analog signals • Digital communication systems • Convert bits to modulated digital signals • Communication system block diagram

  3. Transmitter Communication System Block Diagram Text Images Video • Source encoder converts message into message signal or bits. • Transmitter converts message signal or bits into format appropriate for channel transmission (analog/digital signal). • Channel introduces distortion, noise, and interference. • Receiver decodes received signal back to message signal. • Source decoder decodes message signal back into original message. Source Encoder Source Decoder Channel Receiver

  4. Performance Metrics • Analog Communication Systems • Metric is fidelity • Want m(t)m(t) • Digital Communication Systems • Metrics are data rate (R bps) and probability of bit error (Pb=p(bb)) • Without noise, never make bit errors • With noise, Pb depends on signal and noise power, data rate, and channel characteristics. ^ ^

  5. Data Rate Limits • Data rate R limited by signal power, noise power, distortion, and bit error probability • Without distortion or noise, can have infinite data rate with Pb=0. • Shannon capacity defines maximum possible data rate for systems with noise and distortion • Rate achieved with bit error probability close to zero • In white Gaussian noise channels, C=B log(1+Ps/PN) • Does not show how to design real systems • Shannon obtained C=32 Kbps for phone channels • Get 1.5 Mbps with DSL by using more bandwidth

  6. -T0 0 T0 2T0 Periodic Signals • xp(t) periodic if exists T such that xp(t)=xp(t+T) for all t. • Smallest such T is fundamental period T0 • Any integer multiple of T0 is a period of xp(t) • Fundamental period defined as f0=1/T0 • Aperiodic signals are not periodic

  7. -T0 0 T0 2T0 0 T0 Projection of Signals • Fourier series representation • Project periodic signals onto basis functions • Periodic signal is weighted sum of these functions c2 c1 c3 0 0 T0 T0

  8. Exponential Basis Functions • Fourier series uses exponential basis fcns • Fourier series representation • The {cn}s are the Fourier Series coefficients • These represent the frequency components of the periodic signal.

  9. Main Points • Transmitter converts information into a signal appropriate for transmission, receiver does reverse. • Performance metric for analog systems is fidelity, for digital it is rate and error probability. • Data rates over channels with noise have a fundamental capacity limit. • Fourier series represents periodic signals as a weighted sum of exponential functions. • The Fourier series coefficients are the frequency components of the periodic signal.

More Related