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...
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.
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.
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]...
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:
$$x(t) = a_0 + \sum_{k=1}^{k=N} A_k \cos ( k\omega_0 t + \phi_k)$$
$$x(t) = \sum_{k=0}^{k=N} A_k \cos...
Hi! Thanks for your reply!
Ok rewriting the series like that makes things easier.
However I didn't quite understand your last suggestion, can you explain it again please?
What I thought to do was, using the rewritten series, I would get to
$$x(t) = a_0 + \sum_{k=1}^{k=N} 2A_k \cos (j...
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...
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...
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...
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...
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.
My apologies, the line segment can be described by $$\gamma (t) = (t,1-t)$$ t from 0 to 1.
Then I apply the definition $$ \int F(\gamma (t)) \gamma ' (t) dt$$
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?
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...