Recent content by AVBs2Systems

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    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.
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    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...
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    Semigroup property for convolution

    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}...
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    Semigroup property for convolution

    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...
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    Semigroup property for convolution

    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) =...
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    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...
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    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...
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    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...
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    How to determine the power of this circuit?

    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/
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    Engineering Help finding the damping ratio formula for this 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) =...
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    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...
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    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} +...
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    I Fourier series representation

    Hi Check the dirichlet conditions Any function that satisfies these, has a fourier series rep.
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    Fourier Series = Re(Power Series)

    Hi Joe 1. 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...
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    I Ambiguous Results for two Fourier transform techniques

    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...
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