16 Practical MATLAB® Applications for Engineers
R.1.38 A real exponential discrete sequence is defi ned by the equation of the form
f(n) = acn
where a and c are real constants.
Observe that the sequence given by f(n) can converge or diverge depending on
the value of c (less than or greater than one).
R.1.39 Recall that the general sinusoidal (analog) function is given by
f(t) = A cos(t + )
where A represents its amplitude (real value); ω is referred as the angular frequency
and is given in radian/second; ω = 2 πf, where f is its frequency in hertz, or cycles
per second ( f = 1/T); and α is referred as the phase shift in radians or degrees
(2π rad = 360°) (see Chapter 4 of the book titled Practical MATLAB® Basics for Engi-
neers 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 discrete sequence is defi ned by the following equation:
f(n) = A cos(2n/N + )
f1(t) = 4*e(−t/2) versus tf3(t) = 4*e(−t/2)*u(t) versus t f4(t) = −4*e(−t/2)*u(t) versus tf2(t) = 4*e(t/2) versus t1520151050105− 2 0022 − 20
t (time) t (time)Amplitude [f1(t)] Amplitude [f2(t)]5− 5− 10− 15− 20
− 2 02432− 2 0210Amplitude [f3(t)] Amplitude [f4(t)]t (time)0t (time)FIGURE 1.17
Plots of f 1 (t), f 2 (t), f 3 (t), and f 4 (t) of R.1.37.