PSfrag replacements
EXERCISE 3.4:
Use the Fourier integral to determine all the Fourier Series coefficients of the “sine-cubed” signal. In other words,
evaluate the integral
ZT0
1
sin3 (3πt)e− j (2π/T0 )kt dt
ak =
T0
0
for all k.
Hints: find the period first, so that the integration interval is known. In addition, you might find it easier to convert the
sin3 (·) function to exponential form (via the inverse Euler formula for sin(·)) before doing the Fourier integral on each
of four different terms. If you then invoke the orthogonality property on each integral, you should get exactly the same
answer as (3.29).
McClellan, Schafer and Yoder, Signal Processing First, ISBN 0-13-065562-7.
c 2003 Pearson Education, Inc.
Prentice Hall, Upper Saddle River, NJ 07458. SOLUTION
McClellan, Schafer, and Yoder, Signal Processing First, ISBN 0-13-065562-7.
Prentice Hall, Upper Saddle River, NJ 07458. © 2003 Pearson Education, Inc.