SIGNALS & SYSTEMSQUESTION BANK 21. With regard to Fourier series representation, justify the following statements:a. Odd functions have only sine termsb. Even functions have no sine terms.c. Functions with half-wave symmetry have only odd harmonics.

2. Obtain the Fourier components of the periodic rectangular waveform shown below.

3. Obtain the Fourier components of the periodic square wave signal which is symmetrical with respect to vertical axis at time t = 0 as shown.

4. Determine the Fourier series of the function shown in figure.

5. Find the Fourier series of the wave shown in figure.

6. Determine the Fourier series representation of

7. Use the defining equation for the Fourier series coefficients to evaluate the Fourier series representation for the following signals,

8. Obtain the Fourier series representation of an impulse train given by,

9. Determine the Fourier series expansion for the signal x(t) shown in figure.

10. Assuming T0 = 2, determine the Fourier series expansion of the signal shown in the following figure.

11. State different properties of Fourier series.

12. State the three important Spectral Properties of Periodic Power signals.

13. Write short notes on Dirichlets conditions.

14. Derive polar Fourier series from Exponential Fourier series representation & hence prove that

15. Determine the relation between trigonometric Fourier series and exponential Fourier series. (or) Explain the concept of generalized representation of signal f(t).

16. Determine the exponential form of Fourier series for the waveform in below figure.

17. Show that the Fourier series of a periodic signal with rotational symmetry contain only odd harmonics.

18. a) Represent the function et over the interval (0 < t < 1) by the trigonometric Fourier series and exponential Fourier series.b) Find the exponential Fourier series of the saw tooth waveform shown in fig. plot the magnitude and phase spectrum.

19. Determine the trigonometric and exponential Fourier series of the Function shown in fig.

20.

Prove that the normalized power is given by where are complex Fourier coefficients for the periodic waveform.

21. If find the Fourier coefficient and hence find y(t) such that integral square error is minimised.

22. The complex exponential representation of a signal f(t) over the interval (0, T) is

a) What is the numerical value of T?b) One of the components of f(t) is A Cos 3t. Determine the value of A.c) Determine the minimum number of terms which must be retained is the representation of f(t) i order to include 99.9% of the energy in the interval.

23. Write short notes on exponential Fourier spectrum and the concept of negative frequency.

24. What is meant by Fourier series of non sinusoidal periodic waveform? Explain the significance of the term, half wave symmetry used in determining the Fourier series of the given waveform.A.S.Rao Balaji Institute of Engineering & SciencesPage 4