Lesson_6 - EEL 3135: Signals and Systems Dr. Fred J....

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EEL 3135: Signals and Systems Dr. Fred J. Taylor, Professor Lesson Title: Sampling Lesson Number: 06 (Chapter 4.1- 4.2) Introduction One of the most important scientific advancements of the first half of the twentieth century was attributable to Claude Shannon of Bell Laboratories. Many of Shannon's inventions are with us today, others are forgotten. One of his more amusing creations was a black box which, when activated with a switch, would extend a green hand outwards and turn the switch off. Of greater value is his celebrated and enduring Sampling Theorem (see factoid) Shannon worked for the telephone company and, as such, was interested in maximizing the number of billable subscribers that could simultaneously use a copper telephone line. Shannon’s innovation was to sample the individual subscriber’s conversations, interlace the samples together, place them all on a common telephone wire, finally reconstructed the original message at the receiver after de-interlacing the samples. Today we refer to this process as time-division multiplexing (TDM). Shannon established the rules that govern the sampling and signal reconstruction procedure. Without a reconstruction rule, however, Shannon’s labors would have held no value to the telephone company. Understanding the Sampling Theorem is core to understanding modernsignal processing. The theorem both enables and constrains the performance of the typical discrete-time system suggested in Figure 1. This system consists of an ADC, DAC, digital or DSP processor, plus analog signal conditioning filters ( i.e ., anti-aliasing and reconstruction filter). The Sampling Theorem also motivates the need for these signal conditioning filters. Figure 1: Signal processing (DSP in particular) system consisting of an input signal conditioner (anti-aliasing filter), ADC, DSP microprocessor, DAC, and output signal conditioner (reconstruction filter). Sampling Continuous-time signals where defined in Lesson 1 (Chapter 1). They were also referred to as analog signals. Using a process called sampling; a continuous-time signal can be converted 1
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EEL 3135: Signals and Systems Dr. Fred J. Taylor, Professor into discrete-time signal. In theory, an ideal sampler measures the instantaneous value of a signal x(t), at t=kT s , producing a sample value: x[k]=x(kT s ) 1. The facilitating technology is called a sample and hold circuit which takes a snapshot of the analog signal x(t) at discrete times. The mechanism by which the analog signal x(t) is converted into a set of sample values (called a time-series) is a continuous-to-discrete converter (C to D) A simple model of an electronic sample and hold circuit is shown in Figure 2. Figure 2:
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Lesson_6 - EEL 3135: Signals and Systems Dr. Fred J....

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