Recent content by Mik256

  1. M

    Power signal calculation using Parseval's Theorem

    Firstly, thanks Charles Link and Marcusl for your reply. Unfortunately it was the text of the exercise, then I guess my supervisor made some assumptions. The condition that the biggest ##\tau## is bigger than ##f_c+f_m## is always verified. I then wrote again the expression of ##R##, and...
  2. M

    Power signal calculation using Parseval's Theorem

    Homework Statement Hi guys, I have the following transmitted power signal: $$x(t)=\alpha_m \ cos[2\pi(f_c+f_m)t+\phi_m],$$ where: ##\alpha_m=constant, \ \ f_c,f_m: frequencies, \ \ \theta_m: initial \ phase.## The multipath channel is: $$h(t)=\sum_{l=1}^L \sqrt{g_l} \ \delta(t-\tau_l).$$...
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    Integral of absolute value of a Fourier transform

    Alright, this is my attempt of solution: $$ Y(f)=\frac{\pi}{2} \alpha_m \sum_{l=1}^{L} \sqrt{g_l}\left [ e^{-j(\omega \tau_l - \theta_m)} \delta(\omega - \omega_0) + e^{-j(\omega \tau_l + \theta_m)} \delta(\omega + \omega_0) \right ] $$ $$ \int_0^{f_c+f_m} |Y(f)|^2df= \Big(\frac{\pi}{2}...
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    Integral of absolute value of a Fourier transform

    Yes I am sure about it. Could you briefly explain me why I will get zero? And, if you had an idea to solve it, would you be so kind to sketch me a solution? Thanks for your help!
  5. M

    Integral of absolute value of a Fourier transform

    Homework Statement Hi guys, I am going to calculate the following integral: $$\int_0^{f_c+f_m} |Y(f)|^2\, df$$ where:$$Y(f)=\frac{\pi}{2} \alpha_m \sum_{l=1}^{L} \sqrt{g_l}\left [ e^{-j(\omega \tau_l - \theta_m)} \delta(\omega - \omega_0) + e^{-j(\omega \tau_l + \theta_m)} \delta(\omega +...
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