Periodic Signals
This chapter is devoted to initial fundamental concepts of signal processing. Periodic signals provide a convenient context for this purpose. The chapter is also an introduction to the Signal Processing Toolbox. A number of figures and MATLAB programs hav
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Periodic Signals
1.1 Introduction This chapter is devoted to initial fundamental concepts of signal processing. Periodic signals provide a convenient context for this purpose. The chapter is also an introduction to the Signal Processing Toolbox. A number of figures and MATLAB programs have been included to illustrate the concepts and functions being introduced. This methodology is continued in the next chapters of the book. Some examples include sound output, which contributes for a more intuitive study of periodic signals. Of course, a main reference for this chapter and the rest of the book is the Documentation that accompanies the MATLAB Signal Processing Toolbox. Other more specific references are indicated when opportune in the different sections of the chapter. The most important contents to be considered in the next pages refers to the Fourier transform and to sampling criteria. Both are introduced by way of examples. The Appendix A of the book contains a more formal exposition of these topics, including bibliography. The two final sections of this chapter include Internet addresses of interesting resources, and a list of literature references. The book [3] provides a convenient background for this chapter.
1.2 Signal Representation Suppose you have a signal generator so you have the capability of generating a square wave with 1 Hz frequency. You adjust the generator, so the low level of the signal is 0 v. and the high level is 1 v. Figure 1.1 shows 3 s of such signal: The signal in Fig. 1.1 repeats three consecutive times the same pattern. It is a periodic signal with period T = 1 s. © Springer Science+Business Media Singapore 2017 J.M. Giron-Sierra, Digital Signal Processing with Matlab Examples, Volume 1, Signals and Communication Technology, DOI 10.1007/978-981-10-2534-1_1
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1 Periodic Signals
Fig. 1.1 A square signal
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Suppose you also have a computer with a data acquisition channel, so it is possible to get samples of the 1 Hz square signal. For instance, let us take 10 samples per second. In this case, you get from 3 s of signal, a data set like the following: A = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]; From this data set, with 30 numbers, it is possible to reproduce the signal, provided information about time between samples is given. In order to have such information, another parallel set of 30 sampling times could be recorded when you get the data; or just keep in memory or paper what the sampling frequency was (or the total time of signal that was sampled). Figure 1.2 plots the data set A versus 30 equally spaced time intervals along the 3 s. The MATLAB code to generate Fig. 1.2 is the following: Program 1.1 Square signal % Square signal A=[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,... 1,1,1,1,1,0,0,0,0,0]; fs=10; %sampling frequency in Hz tiv=1/fs; %time interval between samples; t=0:tiv:(3-tiv); %time intervals set (30 values) plot(t,A,'*'); %plots figure axis([0 3 -0.5 1.5]); xlab
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