Chapter3-1

Chapter3-1 - Spring 2009 ELEC001 Electronic &...

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P.1 Chapter 03—Digitization From Signals to Digital Information Spring 2009 ELEC001 Electronic & Information Technology Converting continually changing quantities to a sequence of “integers”
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P.2 Digitization To enjoy the power of the digital ICs and computers we discussed in the last chapter, we need to convert signals into digital forms. A “digital signal” is a set of sampled values represented in binary form as bits . Digitization comprises two conceptual operations: (1) Sampling refers to converting an analog signal (such as music) into a sequence of numbers by measuring the signal at discrete time or space instances. Each number is called a sample and remains continuous in value (2) Quantization refers to putting these samples into binary format (bits), i.e., making them discrete in values. ] [ ) ( n x t x [] d x nx n
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P.3 ADC – Analog-to-Digital Converter What determines sampling rate needed and the number of bits needed to represent each sample? In the next two sections we will study these two concepts: Sampling and Quantization . x(t) ADC x d [n] samples Digital words ADC: analog-to-digital converter Conceptually, this conversion is done by an analog-to- digital converter (ADC)
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P.4 Example of Digitization Therefore, for a 3 minute song, at the sampling rate of 44,100 samples per second and 16 bits per sample, there are a total of 44,100 * 16 * 60 * 3 * 2 = 254,016,000 bits This is equivalent to ~242 Mb or ~30.3 MB (read as “mega bits”) or ~ 10 MB per minute. (1 MB = 8 Mb) Digital music stored on a Compact Disc ( CD )comes from samples that are taken at 44,100 times per second from the original music signal, and each sample is quantized and shored as a 16 bit number . A CD, which provides ~600 MB of storage, can keep about 60 minutes of digital CD music Recall that 1 MB has 2 20 = 1,048,576 bytes
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P.5 Sampling Sampling is the process of recording values (samples) of a signal at distinct points in time or space . e.g. (audio) waveforms are sampled in time . Images are sampled in space . Time-varying scenes (video) are sampled in both time and space . Samples are often observed at uniformly spaced time instants or spatial intervals (e.g. pixels in a digital image). The heights of the dots represent the samples at fixed time intervals.
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P.6 Presumably, samples will eventually be converted back into a continuously form for human consumption Original analog signal s(t) and its samples Sampled signal s(n) Recreating Signal from Samples Re-creating the original analog signal s’(t) time time T s
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P.7 Required Sampling Rate Let us first assume that we can store the samples arbitrarily accurately So the question is how often we should take samples of a waveform or pictures in a video, to ensure that the samples will allow us to faithfully re-create the original information?
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This note was uploaded on 01/28/2011 for the course ELEC 001 taught by Professor Albertwong during the Spring '09 term at HKUST.

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Chapter3-1 - Spring 2009 ELEC001 Electronic &...

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