# Recent content by AVBs2Systems

1. ### How to distinguish between linear and non-linear circuits?

IIRC, 2 things for certain can classify circuits as non-linear: 1. Non linear elements such as diodes. 2. Changing frequency of sources or input waveforms. Mathematically, a linear circuit will obey the superposition principle with regards to signals across the output.
2. ### Semigroup property for convolution

I submitted both the approaches, one with the incorrect fourier transform and the other with the convolution integral. The convolution integral, reduced using partial fraction decomposition or the residue theorem (neither of which I was able to produce as a solution) reduces it to the form...

6. ### Semigroup property for convolution

Summary: Show that for this family of functions the following semigroup property with respect to convolution holds. Hi. My task is to prove that for the family of functions defined as: $$f_{a}(x) = \frac{1}{a \pi} \cdot \frac{1}{1 + \frac{x^{2}}{a^{2}} }$$ The following semigroup property...
7. ### MATLAB Bilinear spline interpolation MATLAB using MESHGRID and SURF

My apologies, $$u_{i , j}$$ Is the matrix, whereas $$\Omega$$ I sismply the cartesian product as the professor has given above. I must say I am very grateful for the time you took to actually write the code, thank you. I will check the details and post the results in a few hours as I am at...
8. ### MATLAB Bilinear spline interpolation MATLAB using MESHGRID and SURF

Hello. So, I must provide a solution for an image processing course I am taking (implemented in MATLAB). The task is as follows: 1. I must provide a MATLAB script that takes in a DISCRETE N x N matrix (Greyscale picture) and does Bilinear spline interpolation on it. This is the spline...

Hi BO. the standard form of second order systems is like this: $$x(t) = y''(t) + 2 \delta y'(t) + \omega_{r}^{2} y(t)$$ I would do a thevenin transform from the point of view of the branch of the inductor and capacitor in series, you get the following thevenin parameters: $$v_{th}(t) =... 11. ### I Why use Epsilon Delta proofs? Hi NockWodz I can say that we use epsilon delta proofs to prove that a limit exists because thats literally the definition of a limit. Hence, to prove that some objects exists or is equal to some other well defined object, the way is to prove that it matches the definition of that object. In... 12. ### I Ambiguous Results for two Fourier transform techniques Yes, I apologise for not being more thorough. So:$$ \Re\big( X(j \omega) \big) = X(j \omega)_{Even} \,\,\,\,\, j \cdot \Im\big(X(j\omega) \big) = X(j \omega)_{odd} $$Here:$$ X(j \omega) = \dfrac{A}{b + j\omega)}= \dfrac{A \cdot(b - j\omega) }{b^{2} + \omega^2} = ´\dfrac{Ab}{b^{2} +...
Hi Painter The Fourier Transform of a function is defined as: $$x(j\omega) = \displaystyle \int_{-\infty}^{\infty} f(t) \cdot e^{-j(\omega t)} \,\,\,\, \text{dt}$$ The trigonometric fourier series for a function is defined as:  f(t) = \dfrac{a_{0}}{2} + \displaystyle \sum_{k=1}^{k \to...