Search results

  1. G

    Bandpass filtering a signal

    I do understand we will only have odd harmonics because we have an odd function...
  2. G

    Bandpass filtering a signal

    By peaks do you mean just maxima? I'm sorry that isn't make sense to me.Why does that work? Also I tried to do what you said and got for all of them 100 Hz (2 peaks for the maximum wave) which doesn't make sense...
  3. G

    Bandpass filtering a signal

    The blue signal is the input signal. The green signal is the output signal, and it's the one in which we're trying to determine the frequency of the sinusoids.
  4. G

    Bandpass filtering a signal

    Hello scottdave! The thing is I don't have an expression for my input signal, only knowing its fundamental frequency. Nothing is said about the filter not being ideal so I assume that yes it is ideal.
  5. G

    Bandpass filtering a signal

    1. Homework Statement So let's say that I have a signal of fundamental frequency 50Hz. I then have a band-pass filter that passes the band between 800 and 1000 Hz of my signal. I don't know the expression of the signals I just know the graphics: [![enter image description here][1]][1]...
  6. G

    Derivation of the Fourier series of a real signal

    Ok, thank you very much for your help!
  7. G

    Derivation of the Fourier series of a real signal

    Or do you think I should simply make A_0 = a_0 ?
  8. G

    Derivation of the Fourier series of a real signal

    Yes sorry that was a typo. But is it incorrect to put k=0 inside the series? Because that was what my professor did when he gave us the exercise.
  9. G

    Derivation of the Fourier series of a real signal

    Oh you're right it is from zero to N! I just realized that now. Now I realize what you meant on incorporating the 2 factor when defining ##A_k##. Then I can simply write the series as: $$x(t) = a_0 + \sum_{k=1}^{k=N} A_k \cos ( k\omega_0 t + \phi_k)$$ $$x(t) = \sum_{k=0}^{k=N} A_k \cos...
  10. G

    Derivation of the Fourier series of a real signal

    Hi! Thanks for your reply! Ok rewriting the series like that makes things easier. However I didn't quite understand your last suggestion, can you explain it again please? What I thought to do was, using the rewritten series, I would get to $$x(t) = a_0 + \sum_{k=1}^{k=N} 2A_k \cos (j...
  11. G

    Derivation of the Fourier series of a real signal

    But I never said that they were equal. I said one is equal to the conjugate of the other which is always true if the signal is real
  12. G

    Derivation of the Fourier series of a real signal

    1. Homework Statement Consider the fourier series of a signal given by $$x(t)=\sum_{k=-\infty}^{\infty} a_ke^{jk\omega_0t}$$ Let's consider an approaches to this series given by the truncated series. $$x_N(t)=\sum_{k=-N}^{N} a_ke^{jk\omega_0t}$$ a- Show that if $x(t)$ is real then the...
  13. G

    Work of a non conservative field

    You mean H(g(t)) (with the vector sign). Because the integral gets complicated.
  14. G

    Work of a non conservative field

    1. Homework Statement Compute the work of the vector field $$H: \mathbb{R^2} \setminus{(0,0}) \to \mathbb{R}$$ $$H(x,y)=\bigg(y^2-\frac{y}{x^2+y^2},1+2xy+\frac{x}{x^2+y^2}\bigg)$$ in the path $$g(t) = (1-t^2, t^2+t-1)$ with $t\in[-1,1]$$ 2. Homework Equations 3. The Attempt at a Solution...
  15. G

    Problem about the derivative of an unknown function

    Is what you mean equivalent to the derivative of a composition of functions? I think I got it. What I did was to differentiate both the equations given obtaining: $$\frac{df}{dx}(t,t) + \frac{df}{dy}(t,t) = 3t^2+1$$ $$\frac{df}{dx}(t,-2t) -2 \frac{df}{dy}(t,-2t) = 2$$ Then making t=0...
  16. G

    Problem about the derivative of an unknown function

    1. Homework Statement $$f:\mathbb{R^2}\to\mathbb{R}$$ a differentiable function in the origin so: $$f(t,t) =t^3+t$$ and $$f(t,-2t)=2t$$ Calculate $$D_vf(0,0)$$ $$v=(1,3)$$ 2. Homework Equations 3. The Attempt at a Solution I have no idea on how to approach this problem. I know that...
  17. G

    Multivariable calculus: work in a line segment

    Looks wrong? What do you mean? Well I know that with other path the the work is still the same (unless the direction was the opposite, in which we would have the opposite sign). I'm going to try then, thanks.
  18. G

    Multivariable calculus: work in a line segment

    My apologies, the line segment can be described by $$\gamma (t) = (t,1-t)$$ t from 0 to 1. Then I apply the definition $$ \int F(\gamma (t)) \gamma ' (t) dt$$
  19. G

    Multivariable calculus: work in a line segment

    Thanks for all the replies. The integral I obtained by definition was $$\int \frac{1}{2t^2-2t+1} dt$$. Any suggestions on how to solve this integral the simplest way?
  20. G

    Multivariable calculus: work in a line segment

    1. Homework Statement Compute the work of the vector field ##F(x,y)=(\frac{y}{x^2+y^2},\frac{-x}{x^2+y^2})## in the line segment that goes from (0,1) to (1,0). 2. Homework Equations 3. The Attempt at a Solution My attempt (please let me know if there is an easier way to do this) I...
Top