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lecture12 - EE455/591 Digital Transm ission Digital Re...

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EE455/591 EE455/591 Digital Transmission Digital Transmission Reading: Section 7.1, 7.2 Reading: Section 7.1, 7.2 Review: Vector Quantizaton Review: Vector Quantizaton Topics: Topics: 1. Shannon Channel Capacity Formula 1. Shannon Channel Capacity Formula 2. Digital Multiplexing 2. Digital Multiplexing 3. Digital Communications System 3. Digital Communications System 4. Pulse Amplitude Modulation (PAM) and Pulse Position 4. Pulse Amplitude Modulation (PAM) and Pulse Position Modulation (PPM) Modulation (PPM)
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Review: Vector Quantization Ex 2: (x 1 , x 2 ) is highly correlated: x 1 uniform in [-1,1] and x 2 = x 1 + u with u uniform in [-¼,¼] We may quantize x 1 and x 2 each by 2 bits. This is bad because we are quantizing a large box where most probability is located within the parallelogram shown We may also quantize x 1 and u separately, but since u has a smaller range, it should require fewer quantization levels, e.g. x 1 is quantized by 3 bits and u by 1 bit The better way is to divide the thin parallelogram into 16 smaller parallelograms as shown below. x 1 x 2 1 -1 ¼ If we quantize by 8 bits, i.e. dividing the parallelogram into 256 regions, then we should use 256 small squares or hexagons to divide the parallelogram. At the boundary, these squares or hexagons may fall outside because they do not fit exactly the parallelogram.
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1. Shannon Channel Capacity Formula For channel of bandwidth W, and SNR S/N, error free transmission is possible for data rate R less than channel capacity C = W log 2 (1 + S/N) Noise power N=N 0 W where ½N 0 = ½kT is the spectral noise power.
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This note was uploaded on 11/01/2009 for the course EEE 455 taught by Professor Hui during the Spring '09 term at ASU.

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lecture12 - EE455/591 Digital Transm ission Digital Re...

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