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In Signal Processing books, a fundamental theorem is that linear time invariant systems can be represented as a convolution with a distribution. Could you give a mathematically rigorous statement of ...

I am currently dealing with discrete Fourier transform and correlation technique to construct the spectrum of a broad band signal. It's already known that if I have enough observations of the signal, ...

Given any $g \in L^\infty(\mathbb{R})$, we define the associated multiplier operator $T_g \colon L^2(\mathbb{R}) \to L^2(\mathbb{R})$ by $$ \mathcal{F}(T_g f) \ = \ g.\mathcal{F}f $$ where $\mathcal{F}...

I would like to know if the Prolate Spheroidal Wavefunctions (PSWFs, defined below) are in $L^1(\mathbb{R})$. I know that they are square integrable, but cannot decide about absolute integrability. ...

For $N$ be a fixed natural number, define $w=e^{\frac{2\pi i}{N}}$ and $z=e^{\frac{\pi i}{N}}$, so that $z^2=w$. Let $D$ be the diagonal matrix $D=\operatorname{diag}(1,z,z^2,\ldots,z^{N-1})$ and $F$ ...

I have a question regarding the possibility of constructing a Discrete Wavelet Transform based on a scaling function having Gaussian decay (and no more decay than that). More specifically, I am ...