# Questions tagged [fourier-transform]

continuous Fourier transform, discrete Fourier transform (DFT), discrete cosine transform (DCT), discrete sine transform (DST)

2,222 questions
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### meaning of double headed arrow

I am studying properties of discrete time Fourier transform and I encountered a notation shown highlighted in attached photo What is meant by this notation? Is it meaning equality? screenshot of ...
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### Analytical expression for PSD

Is it possible to obtain an analytical expression for the PSD? The PSD is defined as follows, $S(\omega) = lim_{T \rightarrow \infty} \frac{1}{T} |Y(\omega)|^2$ Assuming there is $Y(\omega)$ ...
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### fourier series meaning complex radii meaning

I'm talking about the incredible answer from Mark Eichenlaub. Fourier transform for dummies He said : "we must allow the circles to have complex radii. It's the same thing as saying the ...
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### Fourier transform unitary operator

I'm trying to understand why there is a continous extenstion of $\mathcal{F}_0f$ to a unitary operator in $L^2$. So let $\mathcal{F}_0f: S(\mathbb{R}^m) \to S(\mathbb{R}^m).$ This is a bijective ...
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