Q1 10 Given a periodic signal q(t) as shown in Figure Q1.1. -2T q(t) 2 -2 T 2T (a) (b) Figure Q1.1 Determine the trigonometric Fourier series coefficients (ao, an and b) of the signal q(t). Express the signal q(t) in trigonometric Fourier series by considering only the first 3 harmonics. (c) The signal q(t) with the period T = 105s is passed through an LTI system with frequency response given in Figure Q1.2. Determine the output of the system. |H(f)\ 6 -600 600 f(kHz) Figure Q1.2 ZH(f) EIN f(kHz)

Give an example of fourier series even function and it's calculation.

Fourier Analysis is a powerful analytical tool used in engineering. Describe why it is useful and give some physical examples where it may be implemented.What are the limitations of Fourier Analysis and explain the reasons why

1) For the signals shown in below,a) Find the Fourier transform of the half-cosine pulse in figure (a). Sketch amplitude spectrum of the G(f).b) Apply the time-shifting property to the result obtained in part (a) to evaluate the spectrum of the half-sine pulse shown figure (b). Sketch amplitude spectrum of the G(f).c) What is the spectrum of a half-sine pulse in figure (b) having a duration equal to aT ? Sketch amplitude spectrum of the G(f).d) What is the spectrum of the negative half-sine pulse shown in figure (c) ? Sketch amplitude spectrum of the G(f).e) Find the spectrum of the single sine pulse shown in figure (d). Sketch amplitude spectrum of the G(f).

Briefly describe the differences between Fourier Transforms and Discrete Fourier Transforms.

a) Find the Fourier transform of the half-cosine pulse in figure (a). Sketch amplitude spectrum of the G(f). b) Apply the time-shifting property to the result obtained in part (a) to evaluate the spectrum of the half-sine pulse shown figure (b). Sketch amplitude spectrum of the G(f). c) What is the spectrum of a half-sine pulse in figure (b) having a duration equal to aT ? Sketch amplitude spectrum of the G(f). d) What is the spectrum of the negative half-sine pulse shown in figure (c) ? Sketch amplitude spectrum of the G(f). e) Find the spectrum of the single sine pulse shown in figure (d). Sketch amplitude spectrum of the G(f). g(t) g(t) A -T/4 0 T/4 T/2 (a) (b) g(t) g(t) -T/2 -T/2 T/2 -A -A (c) (d)

Q1. Show that the time compression of a periodic signal by a factor of a expands the Fourier spectra by the same factor.

please explain great detail!!   i dont quite understand how to approach this problem a much easier way.!     solve simplier way..

From the idea of the Harmonic analysis light the importance of Fourier transforms in wave generating?

Please take your time and make sure the answer is correct, and show all work. Thank you!