Lecture 12- The Sampling Theorem

Lecture 12- The Sampling Theorem - Lecture 12 ECSE304...

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1 Lecture 12 ECSE304 Signals and Systems II ECSE 304 Signals and Systems II Lecture 12: The Sampling Theorem Reading: O and W - Sections 7.1,7.2,7.3 Boulet – Chapter 15 Richard Rose McGill University Dept. of Electrical and Computer Engineering 2 Lecture 12 ECSE304 Signals and Systems II Course Outline • Discrete-Time Fourier Series and DT Fourier Transform • The Z – Transform • Time and Frequency Analysis of DT Signals and Systems • Sampling Systems – Lecture 12: The Sampling Theorem – Lecture 13: Discrete Time Processing of Continuous Time Signals – Lecture 14: Sampling of Discrete Time Signals • Application to Communications Systems • State Models of Continuous Time LTI Systems • Linear Feedback Systems
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3 Lecture 12 ECSE304 Signals and Systems II • Impulse Train Sampling • The Sampling Theorem • Sampling with Zero Order Hold • Signal Reconstruction Using Interpolation • Aliasing Outline 4 Lecture 12 ECSE304 Signals and Systems II • Impulse Train Sampling – Obtaining discrete sequences from continuous time • The Sampling Theorem – How often must we sample a continuous signal in order to recover it from its samples? • Sampling with Zero Order Hold – A practical way to implement sampling systems • Signal Reconstruction Using Interpolation – Recovering the continuous time signal from samples • Aliasing – What happens if we don’t sample often enough? Outline
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5 Lecture 12 ECSE304 Signals and Systems II • Storing media like Speech/Music/Image/Video in digital form • Transmitting media over digital communications channels • Performing discrete time processing of continuous time signals – Filtering – Enhancement – Modulation / Demodulation Motivations for Obtaining Discrete Time Representations of Continuous Time Signals 6 Lecture 12 ECSE304 Signals and Systems II Sampling Sinusoidal Signals Sinusoid with frequency 100 Hz ( rad/sec) Samples of sinusoid with sampling freq. 2000 s fH z = 200 π Samples of sinusoid with sampling freq. 500 s z = 20 samples per period 5 samples per period
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7 Lecture 12 ECSE304 Signals and Systems II Analog to Digital Conversion Given signal x(t) with amplitude ranging from –V to +V Sample the signal periodically every T seconds Quantize
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This note was uploaded on 02/08/2012 for the course ECSE 304 taught by Professor Chenandbacsy during the Spring '11 term at McGill.

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Lecture 12- The Sampling Theorem - Lecture 12 ECSE304...

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