Case studies for CT systems - Continuous and Discrete Time Signals and Systems - page 368

CHAPTER

8

Case studies for CT systems

Several aspects of continuous-time (CT) systems were covered in Chapters
3-7. Among the concepts covered, we used the convolution integral in
Chapter 3 to determine the output y ( t ) of a linear time-invariant, continuous-
time (LTIC) system from the input signal x ( t ) and the impulse response h ( t ).
Chapters 4 and 5 defined the frequency representations, namely the CT Fourier
transform (CTFT) and the CT Fourier series (CTFS) and evaluated the out-
put signal y ( t ) of the LTIC system in the frequency domain. The CTFT was
also used to estimate the frequency characteristics of the LTIC system by plot-
ting the magnitude and phase spectra. Chapter 6 introduced the Laplace trans-
form widely used as an alternative for the CTFT in control systems, where
the analysis of the transient response is of paramount importance. Chapter 7
presented techniques for designing LTIC systems based on the specified fre-
quency characteristics. When an LTIC system is described in terms of its fre-
quency characteristics, it is referred to as a frequency-selective filter. Design
techniques for four types of analog filters, lowpass filters, highpass filters, band-
pass filters, and bandstop filters, were also covered in Chapter 7. In this chap-
ter, we provide applications for the LTIC systems. Our goal is to illustrate
how the tools developed in the earlier chapters can be utilized in real-world
applications.
The organization of this chapter is as follows. Section 8.1 considers analog
communication systems. In particular, we illustrate the use of amplitude modu-
lation in communication systems for transmitting information to the receivers.
Based on the CTFT, spectral analysis of the process of modulation provides
insight into the performance of the communication systems. Section 8.2 intro-
duces a spring damper system and shows how the Laplace transform is useful
in analyzing the stability of the system. Section 8.3 analyzes the armature-
controlled, direct current (dc) motor by deriving its impulse response and trans-
fer function. The immune system of humans is considered in Section 8.4. Ana-
lytical models for the immune system are considered and later analyzed using
the simulink toolbox available in M ATLAB .

368