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Unformatted text preview: EE 3120 Chapter 3 Introduction to Discrete Time Signals and Systems Sampling C/D DT system D/C x ( t ) x [ n ] ( ) y t y [ n ] CT signal is sampled to convert to a DT signal Signal is processed by a DT system. CT signal constructed from the output sequence We can use a DT system to process a CT signal by sampling the CT signal and applying the resulting sequence to the DT systems, then constructing the output CT signal from the output sequence . ( ) y t y [ n ] Why Sample? Digital signals and systems have many benefits over analog signals. • Less sensitive to changes in component and signal variations caused by temperature, manufacture tolerance. • Circuits can be easily duplicated, built in high volume for low cost and built on a single chip using VLSI circuits • Hardware implementation of digital filters using microprocessors and LSI • Digital filters can be programmed and changed easily, more variety of filtering • Digital signals can be stored in memory, accessed remotely • D sigs can be coded low bit errors and encrypted for privacy • D sys can be timeshared allowing for multiple inputs simultaneously (Time division multiple access, TDMA) • Reproduction of D sigs can be done with NO deterioration or noise added. (photocopying an image vs. scanning) • CPU speeds allow for faster and more complex (real time) digital signal processing, DSP Sampling an Analog Signal Consider an analog f(t) signal defined for all t in ( , ) sampling f(t) with sampling period or sampling rate T gives a discrete time (DT) signal: , where n is an integer ranging from to Define: is a sequence of numbers assumes T = 1 DT signals are also called sequences. . f [n] f [ n ]:= f ( nT ) f ( nT ) Example: is sampled every T = 0.1 seconds. The DT sequence would be: ( ) t x t e = 0.1 ( ) [ ] t n t nT x nT e e x n = = = = ( ) t x t e = [ ] x n Plotted for t from 2 and 2 Plotted for n from 20 to 20 t = 0 nT = 0 t n How often should we sample? • The sampling rate should be selected so that the primary shape of the signal is maintained. T = .01 T = .02 T = .08 4 cycles 1 cycle Chapter 3 Frequencies of Analog and Digital Sinusoids ( ) sin o f t t ϖ = 2 o P π ϖ = T [ ]: ( ) sin o f k f kT kT ϖ = = 0, 1, 2,... k = Analog sinusoid is periodic with fundamental (smallest) period P where: (repeats itself every P seconds) If we sample f ( t ) with a sampling rate: This is a discretetime sinusoid. for [ ] f k...
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This note was uploaded on 02/06/2012 for the course EE 2120 taught by Professor Aravena during the Fall '08 term at LSU.
 Fall '08
 ARAVENA

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