# lecture10 - Lecture Outline(Week 5 lecture 2 Digitizing...

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Lecture Outline (Week 5, lecture 2) Digitizing Analog Signals - Quantization Reading: text1 4.3.1 Supplementary: Text2 6.5.1 Material covered: 1. Nyquist Sampling Theorem Re-examined Sampling at transmitter and low pass filtering at receiver: - - = n nT t T nT t T nT x t x ) ( )) ( sin( ) ( ) ( ~ π π Sampling of signal by impulse train Time Domain Frequency Domain Signal reconstruction: ) ( ) ( ~ t x t x = if 0 | ) ( | f X only for W f | | and W T f s 2 / 1 = . Time Domain (Interpolation) Frequency domain (LP filtering) For a signal with highest frequency f , it is sufficient to sample 2 f times per second Each sample, an analog value, is converted into a digital value For speech of 4KHz, we sample 8000 times per second. Each sample is digitized into 8 bits, yielding a bit stream at 64Kb/s. 2. Scalar Quantization 1

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Why quantization? Finite precision is sufficient Infinite precision destroyed by channel noise. Reliable reproduction of bits Consecutive sampled values are quantized into finite ( N ) number of values.
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