Shannon's Sampling Theorem

Advanced Control Theory on Topic of the Shannon's Sampling Theorem.
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1. SHANNON’S SAMPLING THEOREM PREPARED BY KETAN NAYAK (140413117005) HARSH PARMAR (140413117006) ADVANCED CONTROL THEORY UNDER GUIDANCE OF PROF. JANKI CHOTAI

2. INDEX Sr. NO TOPIC 1. INTRODUCTION 2. STATEMENT 3. SPECTRUMS 4. EFFECT OF ALIASING 5. BAND LIMITING LOW PASS FILTER

3. INTRODUCTION Sampling Theorem was Introduced to Communication Theory in 1949 by Shannon. The Sampling Theorem States that the Higher Number of Samples the Closer its Representation. No of Samples depend on Sampling Rate and Maximum Frequency of the Signal to be Sampled.

4. STATEMENT If a Finite Energy Signal x(t) contains Frequency Higher than “W” Hz then It is Completely determined by Specifying its Values at Instants of Time Which are Spaced (½) Second Apart. If a Finite Energy Signal x(t) contains No Frequency components higher than W Hz then it may be Completely Removed from its Samples which are Spaced (½)w Second Apart.

5. COMBINED STATEMENT A Continuous Time Signal x(t) can be completely represented in its sampled form and recovered back from sampled form if the Sampling Frequency Fs ≥ 2W where w is Maximum Frequency of Continious Time Signal x(t).

6. SPECTRUMS

7. EFFECT OF ALIASING

8. BAND LIMITING LOW PASS FILTER BAND LIMITING LOWPASS FILTER SAMPLER Xs (t) X(t) Strictly Bandlimited