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 deinterlacing the samples.
Today we refer to this process as
timedivision 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 discretetime system
suggested in Figure 1. This system consists of an ADC, DAC, digital or DSP processor, plus
analog signal conditioning filters (
i.e
., antialiasing 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
(antialiasing filter), ADC, DSP microprocessor, DAC, and output signal conditioner
(reconstruction filter).
Sampling
Continuoustime signals where defined in Lesson 1 (Chapter 1).
They were also referred to as
analog signals.
Using a process called sampling; a continuoustime signal can be converted
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentEEL 3135: Signals and Systems
Dr. Fred J. Taylor, Professor
into discretetime 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 timeseries) is a continuoustodiscrete converter (C to D)
A simple model of an electronic sample and hold circuit is shown in Figure 2.
Figure 2:
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 ?
 Digital Signal Processing, Claude Shannon, Dr. Fred J. Taylor, Dr. Fred J., Fred J. Taylor

Click to edit the document details