Recent content by AVBs2Systems

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.

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...

Scaling property and linearity property. Note a and b are greater than zero. The Fourier transform of $$ \mathcal{F} \bigg \{ \frac{1}{1 + {(\frac{x}{a})}^{2} } \bigg \} = \frac{1}{|a|}\cdot \sqrt{ \frac{\pi}{2} } \cdot e^{-|\frac{\omega}{a} | } $$ Hence: $$ \frac{1}{a \pi} \cdot \mathcal{F}...

Hi The Fourier transform of: $$ \mathcal{F} \bigg\{ \frac{1}{a \pi} \cdot \frac{1}{1 + { \frac{x}{a} }^{2} } \bigg \} =\frac{1}{ a^2 \pi} \cdot \sqrt{ \frac{\pi}{2} } \cdot e^{-| \frac{\omega}{a} |} $$ My idea is that, since, the Fourier transform of the convolution results in a mulitplication...

The convolution is defined on $$ l^{1}(\mathbb{Z}) $$ and $$ l^{1}(\mathbb{R} ) $$ spaces. Respectively, for continuous and discrete (absolutely integrable and absolutely summable functions): $$ x[n] * y[n] = \displaystyle \sum_{k \in \mathbb{Z} } x[k] \cdot y[n - k] $$ And $$ x(t) * y(t) =...

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...

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...

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 function...

Hi I thought I might add this quick and easy online circuit simulator, that would help you when practicing questions: https://www.falstad.com/circuit/

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) =...

Hi NockWodz I can say that we use epsilon delta proofs to prove that a limit exists because that's 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...

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 Check the dirichlet conditions Any function that satisfies these, has a Fourier series rep.

Hi Joe1. There exist algebraic methods for DC (constant ) and sinusoidal functions (sinusoidal steady state analysis) in circuits, to find voltage and current and power. There does not exist any algebraic method for non sinusoidal, non DC functions, like triangles, square waves, bipolar waves...

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...