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Introduction  1.9

                        Many of my professional colleagues have made the suggestion that analog
                      modulation concepts should be removed from the modern undergraduate cur-
                      riculum. Comments such as “We do not teach about vacuum tubes so why should
                      we teach about analog modulations?” are frequently heard. I heartily disagree
                      with this opinion but not because I have a fondness for analog modulation but
                      because analog modulation concepts are so important in modern communica-
                      tion systems. The theory and notation for analog signals learned in this text is a
                      solid foundation for further explorations into modern communication systems
                      because modern digital communications use analog waveforms. For example,
                      in the testing of modern communication systems and subsystems analog modu-
                      lation and demodulation concepts are used extensively. In fact, most of my good
                      problems for the analog communication chapters have come as a result of my
                      work in experimental wireless communications even though my research work
                      has always been focused on digital communication systems! Another example
                      of the utility of analog communications is that I am unaware of a synthesized
                      signal generator that does not have an option to produce amplitude modulated
                      (AM) and frequency modulated (FM) test signals. While modern communica-
                      tion engineers do not often design analog communication systems, the theory is
                      still a useful tool. Consequently, this part of the book focuses on analog commu-
                      nications but using a modern perspective that will provide students the tools
                      to flourish in their careers.


          1.5.3 Noise in Communication Systems
                      Understanding the effects of noise and interference on communication systems
                      what makes a communication system engineer uniquely trained. I have always
                      been struck by the fact that engineering technicians have a training in time
                      domain analysis, Fourier analysis, modulation techniques, and demodulation
                      techniques. The main thing a technician does not understand is how to char-
                      acterize how noise impacts the trade-offs that must be made in system design.
                      On the other hand, the understanding of noise is often a frustrating subject for
                      students as the level of mathematics and abstraction can often seem not worth
                      the gains in useful skills. The approach taken in this text is to introduce the
                      minimal amount of abstraction necessary to get useful results for engineering
                      practice.
                        There are four topics/chapters that are presented in this section to introduce
                      the techniques to analyze the impact of noise and interference. The first chapter
                      focuses on the characterization of Gaussian stationary random processes and
                      how linear filters impact this characterization. This material builds heavily on
                      probability and random variable concepts. This text offers little new insights
                      than has been available since the 1950s [DR87, Pap84] other than a reordering
                      of topic presentation. The next chapter generalizes the concepts of random pro-
                      cesses to the case of noise in bandpass communication receivers. The impact of
                      filters in the receiver on the noise characteristics is explored. After these prelim-
                      inary tools are in place, a revisiting of all the forms of analog communications in
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