# Tagged Questions

Fourier analysis, also known as spectral analysis, encompasses all sorts of Fourier expansions, including Fourier series, Fourier transform and the discrete Fourier transform (and relatives). The non-commutative analog is (representation-theory).

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### CT fourier Transform Proof

I am confused trying to understand the Proof of Fourier Transform from Oppenheim book Signals and Systems. I am pasting the equations directly from the book: ...
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I have a question concerning the subspace $\mathcal{S}'_h$ of tempered distributions defined by $u\in\mathcal{S}'_h\Leftrightarrow\lim_{\lambda\rightarrow\infty}\Vert\theta(\lambda ... 0answers 34 views ### Convergence of the sum of fourier coefficients I have a function$f$defined on$[-\pi, \pi]$,$f(\pi) = f(-\pi)$, and has continuous first derivative. How can I prove that the sum of the absolute value of the Fourier coefficients converges? The ... 0answers 37 views ### Finding a Fourier pair satisying some conditions I want to find a Fourier pair$(r,\hat{r})$satisfying some conditions listed below and making$\hat{r}(0)$as small as possible. The requirements for$(r,\hat{r})$:$r,\hat{r}\in L^1(\mathbb{R})$, ... 0answers 35 views ### Eigenfunctions of a 4th Order PDE on 2D domain What technique would you use to find the eigenfunctions of this problem? $$\nabla^2(\nabla^2 u) = 10$$$0 < y < G0 < x < L$With Pure Homogeneous Dirichlet boundary conditions and ... 0answers 28 views ### Piecewise linear approximation of a (low order) trigonometric polynomial, with quantization The Problem Given a trigonometric polynomial of order$K$: $$y(t)=\sum_{k=-K}^K c_k \ e ^ {j k \bar \omega t} \ , \qquad c_{-k}=\bar c_k$$ we want to find the best approximation to it using a ... 0answers 122 views ### wave front set - directions of singularities I am learning about the wave front set of a distribution but am having difficulty understanding some details, which to me seem counter intuitive. We know the fourier transform of a smooth function ... 0answers 45 views ### Fourier transforms of distributions I am reading a proof claiming that every partial differential operator$P(D)$has a fundamental solution$E$. It says that "if we have a distribution$u$on$R^n$with$u(P(D)\phi)=\phi(0)$for ... 0answers 66 views ### A continuous function whose Fourier Series diverges I have read several times that there exist many continuous functions whose Fourier series diverge at some points (sometimes even on a dense subset of the domain!). I tried to find an explicit example ... 0answers 29 views ### I have derived a short proof that answers 'DTFT assumes the sequence to be periodic and hence the expression for the same'. Does my proof make sense? Define: Function '$f$' defined at all (-oo, oo).$U(to)$is a step function that equals 1 when$t \geq to\sum_{n \epsilon Z}\delta(t - nT)$is an impulse train that is non-zero for all$t = nT|{n ...
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Could someone please explain how they got from the first step to the next? I have no idea how the second step follows...