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Unformatted text preview: Sampling Theory Revisited ECE4305: SoftwareDefined Radio Systems and Analysis Professor Alexander M. Wyglinski Department of Electrical and Computer Engineering Worcester Polytechnic Institute Lecture 4 Professor Alexander M. Wyglinski ECE4305: SoftwareDefined Radio Systems and Analysis Sampling Theory Revisited Sampling Theory Revisited USRP Data Flow Signal Types I Analog signal: continuous in time and amplitude I Voltage, current, temperature I Digital signal: discrete both in time and amplitude I Attendance of this class, digitized analog signals I Discretetime signal: discrete in time and continuous in amplitude I Hourly change of temperature in Worcester Professor Alexander M. Wyglinski ECE4305: SoftwareDefined Radio Systems and Analysis Sampling Theory Revisited Sampling Theory Revisited USRP Data Flow Sampling Theory I Sampling is a continuous to discretetime conversion I Most common sampling is periodic I x [ n ] = x c ( nT ) < n < I T is the sampling period in second I f s = 1 / T is the sampling frequency in Hz I Sampling frequency in radianpersecond = 2 f s rad/sec I Use [ ] for discretetime and ( ) for continuoustime signals I This is the ideal case, not the practical, but close enough I In practice, it is implemented with an analogtodigital converter I We get digital signals that are quantized in amplitude and time Professor Alexander M. Wyglinski ECE4305: SoftwareDefined Radio Systems and Analysis Sampling Theory Revisited Sampling Theory Revisited USRP Data Flow Sampling Theory I In general, sampling is not reversible I Given a sampled signal, one can fit infinite continuous signals through the samples I Fundamental issue in digital signal sampling I If we lose information during sampling, we cannot recover it I Under certain conditions, an analog signal can be sampled without loss so that it can be reconstructed perfectly Professor Alexander M. Wyglinski ECE4305: SoftwareDefined Radio Systems and Analysis Sampling Theory Revisited...
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 Spring '10
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