Review of Analog Signal Processing Basics - Digital Signal Processing: Fundamentals and Applications - page 801

B.4 PROBLEMS
B.1. Develop equations for the amplitude spectra, that is, A n (one-sided) and jc n j (two-sided), of
the pulse train xðtÞ displayed in Figure B.13 , where s ¼ 10 m sec.
a. Plot and label the one-sided amplitude spectrum up to 4 harmonic frequencies including
DC.
b. Plot and label the two-sided amplitude spectrum up to 4 harmonic frequencies including
DC.
B.2. In the waveform shown in Figure B.14 , T 0 ¼ 1 ms and A ¼ 10. Use the formula in Table
B.1 to write a Fourier series expansion in magnitude-phase form. Determine the frequency f 3
and amplitude value of A 3 for the third harmonic.
B.3. In the waveform shown in Figure B.15 , T 0 ¼ 1 ms, s ¼ 0 : 2 ms, and A ¼ 10.
a. Use the formula in Table B.1 to write a Fourier series expansion in magnitude-phase form.
b. Determine the frequency f 2 and amplitude value of A 2 for the second harmonic.
B.4. Find the Fourier transform XðuÞ and sketch the amplitude spectrum for the rectangular pulse
xðtÞ displayed in Figure B.16 .
B.5. Use Table B.3 to determine the Fourier transform for the pulse in Figure B.17 .
B.6. Use Table B.3 to determine the Fourier transform for the pulse in Figure B.18 .
B.7. Determine the Laplace transform XðsÞ for each of the following time domain functions using
the Laplace transform in Table B.5 .
FIGURE B.13
Pulse train in Problem B.1.
FIGURE B.14
Square wave in Problem B.2.