Sampling & PCM (new)

# Sampling & PCM (new) - SAMPLING We live in a...

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1 SAMPLING We live in a continuous-time world: most of the signals we encounter are CT signals, e.g. x(t). How do we convert them into DT signals x[n]? —Sampling, taking snap shots of x(t) every T seconds. T : sampling period x[n] x(nT), n= . .., -1, 0, 1, 2, . .. —regularly spaced samples How do we perform sampling? 1

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2 Why/When Would a Set of Samples Be Adequate ? Observation: Lots of signals have the same samples By sampling we throw out lots of information all values of x(t) between sampling points are lost. 2
3 Key Question for Sampling : Under what conditions can we reconstruct the original CT signal x(t) from its samples ? 3

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4 The Sampling Theorem 4 2πB 2πB
5 Impulse sampling (instantaneous sampling ) 2π/T s ω

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6
7 Sampling a signal in time domain makes the spectrum of the signal periodic in frequency domain The sampling process is basic to digital communications 7

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8 N.B.: Overlapping must be avoided in order to recover the information
9 Under sampling and Aliasing

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10 f s = 2B is the Nyquist rate
11 By passing the sampled signal through an ideal low pass filter band-limited to B Hz, the signal is reconstructed exactly from its samples.

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12
13 A different point of view for the interpolation process (time domain)

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14 The previous filter is known as zero order hold filter and is an approximation for the ideal low pass filter. Note that both filters are not realizable [ the first one is band limited in frequency and the other one is non causal]
15 Practical Sampling

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16
17 Applications of the sampling theorem Allows to replace a continuous time signal by a discrete sequence of numbers.

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## This note was uploaded on 03/19/2012 for the course ELCN 306 taught by Professor Hebatmourad during the Spring '10 term at Cairo University.

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Sampling & PCM (new) - SAMPLING We live in a...

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