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
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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
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5 Impulse sampling (instantaneous sampling ) 2π/T s ω
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6
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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
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9 Under sampling and Aliasing
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10 f s = 2B is the Nyquist rate
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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
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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]
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15 Practical Sampling
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16
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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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