Miscellaneous Exercises - Digital Signal Processing: An Introduction with MATLAB and Applications - page 291

Appendix B: Miscellaneous Exercises

Miscellaneous DSP Exercises—A

Q1: Explain the meaning of a ''signal''. Give five examples of real-life signals.

Q2: State five classes of signals with brief explanations.

Q3: Draw a block diagram for an analog/digital signal processing system.

Q4: Show whether the Hilbert transform [that gives constant 90 phase shift for

all sinusoidal signals of the form x(t) = sin(xt + c)] is:
(a) Memoryless, (b) causal, (c) linear, (d) time-invariant, (e) BIBO stable.

Q5: Define the Dirac delta function. How can we approximate it in applications?

Q6: How can we represent an analog system and its I/O relationship?

Q7: Both Fourier and Laplace Transforms are used to represent analog systems.

Which one is the more general?

Q8: State the conditions in the time-domain that an analog system is BIBO

stable. What are the equivalent conditions in the frequency domain?

Q9: Explain what is the physical meaning of the cross-correlation integral. State

an application for this integral.

Q10: What kind of signals can Fourier series represent? Is the Fourier series a

frequency transform? Can it reveal the frequency content of the signal?

Q11: How does the trigonometric Fourier series of an odd periodic signal look

like?

Q12: Can we use Fourier series to represent energy signals?

Q13: Can we use Fourier transform to represent periodic signals? How?

Q14: From the basic definition of Fourier transform, find and plot the amplitude

and phase spectra of the signal x(t) = exp(-5t)u(t). Is this an energy or
power signal? Why?

Q15: What is meant by the duality of the Fourier transform?

Q16: Using Tables, find the Fourier transform of the following signals and plot

their magnitude spectra:
1. sin(2t + 1), 2. cos(5t), 3. 1, (4) d(t), 5. u(t), 6. sgn(5t), 7. P 1 (t), 8.
sinc(t - 5), 9. sinc(t) cos(20t).