Fiber Optic Tutorials

This is a continuation from the previous tutorial - representation of aperiodic signals with continuous-time Fourier transform.   In the previous tutorial, we introduced the Fourier transform representation and gave several examples. While our attention in that tutorial was focused on aperiodic signals, we can also develop Fourier transform representations for periodic signals, thus allowing us to consider both periodic and aperiodic signals within a unified context. In fact, as we will see, we can construct the Fourier transform of a periodic signal directly from its Fourier series representation. The resulting transform consists of a train of impulses in the frequency domain, with...

This is a continuation from the previous tutorial - examples of discrete-time filters described by difference equations.   In the last few tutorials, we developed a representation of periodic signals as linear combinations of complex exponentials. We also saw how this representation can be used in describing the effect of LTI systems on signals. In this tutorial, we extend these concepts to apply to signals that are not periodic. As we will see, a rather large class of signals, including all signals with finite energy, can also be represented through a linear combination of complex exponentials. Whereas for periodic signals...

This is a continuation from the previous tutorial - examples of continuous-time filters described by differential equations.   As with their continuous-time counterparts, discrete-time filters described by linear constant-coefficient difference equations are of considerable importance in practice. Indeed, since they can be efficiently implemented in special- or general-purpose digital systems, filters described by difference equations are widely used in practice. As in almost all aspects of signal and system analysis, when we examine discrete-time filters described by difference equations, we find both strong similarities and important differences with the continuous-time case. In particular, discrete-time LTI systems described by difference equations...

This is a continuation from the previous tutorial - filtering.   In many applications, frequency-selective filtering is accomplished through the use of LTI systems described by linear constant-coefficient differential or difference equations. The reasons for this are numerous. For example, many physical systems that can be interpreted as performing filtering operations are characterized by differential or difference equations. A good example of this that we will examine in later tutorials is an automobile suspension system, which in part is designed to filter out high-frequency bumps and irregularities in road surfaces. A second reason for the use of filters described by...

This is a continuation from the previous tutorial - Fourier series and LTI systems.   In a variety of applications, it is of interest to change the relative amplitudes of the frequency components in a signal or perhaps eliminate some frequency components entirely, a process referred to as filtering. Linear time-invariant systems that change the shape of the spectrum are often referred to as frequency-shaping filters. Systems that are designed to pass some frequencies essentially undistorted and significantly attenuate or eliminate others are referred to as frequency-selective filters. As indicated by eqs. (3.124) and (3.131) [refer to the Fourier series...