[...]... scaled) is defined by  At for t Ն t0 Ar(t Ϫ t0 ) ϭ   0 for t Ͻ t0 where A represents the ramp’s slope and t0 is the time shift with respect to the origin R.1.29 The discrete ramp sequence denoted by r(n − m) u(n − m) is defined analytically by n for n Ն m r(n Ϫ m) u(n Ϫ m) ϭ   0 for n Ͻ m CRC_47760_CH001.indd 13 7/25/2008 4:16:12 PM Practical MATLAB Applications for Engineers 14 R.1.30 The analog... xlabel(‘t (time)’) ylabel(‘Amplitude[f4(t)]’) ; ; The script file exponentials is executed and the results are shown in Figure 1.17 * See Chapter 7, Practical MATLAB Basics for Engineers CRC_47760_CH001.indd 15 7/25/2008 4:16:13 PM Practical MATLAB Applications for Engineers 16 f1(t) = 4*e(−t/2) versus t f2(t) = 4*e(t/2) versus t 20 15 Amplitude [f2(t)] Amplitude [f1(t)] 15 10 5 10 5 t (time) 0 −2 t (time)... phase shift in radians or degrees (2π rad = 360°) (see Chapter 4 of the book titled Practical MATLAB Basics for Engineers for additional details) R.1.40 Recall that sinusoidal and exponential functions are related by Euler’s identities; introduced and discussed in Chapter 4 of the book titled Practical MATLAB Basics for Engineers, and repeated as follows: ejwt = cos(wt) + j sin(wt) R.1.41 A sinusoidal... analytically by  A for n Ն m Au(n Ϫ m) ϭ   0 for n Ͻ m CRC_47760_CH001.indd 11 7/25/2008 4:16:12 PM Practical MATLAB Applications for Engineers 12 pul(t/ ) u(n − m) 1 A n − /2 m −1 m m +1 m +2 m +3 t 0 /2 FIGURE 1.14 Plot of pul(t/τ) FIGURE 1.13 Plot of u(n − m) R.1.24 The analog pulse function pul(t/τ) is illustrated graphically in Figure 1.14 The function pul(t/τ) is defined analytically by  1 for Ϫ / 2... 4:16:11 PM Practical MATLAB Applications for Engineers 10 u(t) 1 t 0 FIGURE 1.9 Plot of the step function u(t) The discrete shifted impulse function δ(n − m)m − 1 … m … m + 1n is defined as 1 for n ϭ m ( n Ϫ m) ϭ  0 for n m R.1.18 Let us go back to the analog world The analog unit step function denoted by u(t) is illustrated in Figure 1.9 Analytically, the analog unit step is defined by 1 for t Ն... instantaneous changes of the information signal CRC_47760_CH001.indd 21 7/25/2008 4:16:14 PM Practical MATLAB Applications for Engineers 22 Phase shift keying (PSK) is a special case of PM signals, in which the phase of the analog high-frequency carrier is varied in accordance with the information signal that is digital in nature PM and FM are commonly referred to as angle modulation (for obvious reasons) R.1.62... color insert following page 374.) Plots of the Laguerre family of R.1.51 CRC_47760_CH001.indd 19 7/25/2008 4:16:14 PM Practical MATLAB Applications for Engineers 20 R.1.52 The family of time-shifted sinc functions are given by sincn(t) = sin(t − n )/[ (t − n )] for n = 0, ±1, ±2, …, ±∞ forms and orthonormal family, over the range −∞ ≤ t ≤ +∞, and are referred to as the sinc family R.1.53 The first five... Chapter 4 of Practical MATLAB Basics for Engineers CRC_47760_CH001.indd 14 7/25/2008 4:16:13 PM Time Domain Representation of Continuous and Discrete Signals 15 the system differential equation.* Note also that when b is complex, then by Euler’s equalities f(t) presents oscillations Finally, the more common equation f(t) = Ae−bt u(t) is defined analytically by  AeϪbt f (t) ϭ  0 for t Ն 0 for t Ͻ 0... temperature Atmospheric humidity Atmospheric pressures or depressions Wind speed • Seismic waves • Tsunamis • Volcanic activity 1 CRC_47760_CH001.indd 1 7/25/2008 4:16:08 PM Practical MATLAB Applications for Engineers 2 To a physician, it may be For a telecommunication engineer, it may be • An electrocardiogram (EKG) • An electroencephalogram (EEG) • A sonogram • • • • Audio sound wave (human voice or music)... interval or the sampling period (also referred to as Ts) CRC_47760_CH001.indd 3 7/25/2008 4:16:09 PM Practical MATLAB Applications for Engineers 4 1.2 Objectives After completing this chapter the reader should be able to • Mathematically define the most important analog and discrete signals used in practical systems • Understand the sampling process • Understand the concept of orthogonal signal • Define . Basics for Engineers Practical MATLAB ® Applications for Engineers CRC_47760_fm.indd iiCRC_47760_fm.indd ii 7/28/2008 12:32:49 PM7/28/2008 12:32:49 PM PRACTICAL MATLAB ® FOR ENGINEERS PRACTICAL MATLAB ® APPLICATIONS. alt="" PRACTICAL MATLAB ® APPLICATIONS FOR ENGINEERS CRC_47760_fm.indd iCRC_47760_fm.indd i 7/28/2008 12:32:49 PM7/28/2008 12:32:49 PM Handbook of Practical MATLAB ® for Engineers Practical MATLAB ® . are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Kalechman, Misza. Practical MATLAB applications for engineers /