Question

(i) Recall that the complex Fourier series of f(x) on [-p/2, p/2] is defined as f(x) = sum_{n=-infty}^{infty} d_n e^{inw_0x} where d_n = frac{1}{p} int_{-p/2}^{p/2} f(x)e^{-inw_0x} dx (1) for n = 0, pm 1, pm 2, dots and w_0 = 2pi/p. What is the Fourier transform of Eq. (1)? Hint 1: Since the Fourier series coefficient d_n is a constant of frequency w, it can be moved out from the integral of the Fourier transform. Hint 2: Make use of the result from Question 4(iii) to solve the Fourier transform. (ii) Using your answer in (i), what is the Fourier transform of a periodic pulse train x[n] with period T_0 (see the figure below). Derive your answer and plot it on the frequency domain.

          (i) Recall that the complex Fourier series of f(x) on [-p/2, p/2] is defined as
f(x) = sum_{n=-infty}^{infty} d_n e^{inw_0x} where d_n = frac{1}{p} int_{-p/2}^{p/2} f(x)e^{-inw_0x} dx (1)
for n = 0, pm 1, pm 2, dots and w_0 = 2pi/p. What is the Fourier transform of Eq. (1)?
Hint 1: Since the Fourier series coefficient d_n is a constant of frequency w, it can be moved out from the integral of the Fourier transform.
Hint 2: Make use of the result from Question 4(iii) to solve the Fourier transform.
(ii) Using your answer in (i), what is the Fourier transform of a periodic pulse train x[n] with period T_0 (see the figure below). Derive your answer and plot it on the frequency domain.

$(i) Recall that the complex Fourier series of f(x) on [-p/2, p/2] is defined as f(x) = sumn=-infty^infty dn e^inw0x where dn = frac1p int-p/2^p/2 f(x)e^-inw0x dx (1) for n = 0, pm 1, pm 2, dots and w0 = 2pi/p. What is the Fourier transform of Eq. (1)? Hint 1: Since the Fourier series coefficient dn is a constant of frequency w, it can be moved out from the integral of the Fourier transform. Hint 2: Make use of the result from Question 4(iii) to solve the Fourier transform. (ii) Using your answer in (i), what is the Fourier transform of a periodic pulse train x[n] with period T0 (see the figure below). Derive your answer and plot it on the frequency domain.$

Added by Mariano C.

Question

Please give Ace some feedback