# Tag Info

### Is there any practical application for performing a double Fourier transform? ...or an inverse Fourier transform on a time-domain input?

No, taking the Fourier transform twice is equivalent to time inversion (or inversion of whatever dimension you're in). You just get $x(-t)$ times a constant which depends on the type of scaling you ...
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### Is there any practical application for performing a double Fourier transform? ...or an inverse Fourier transform on a time-domain input?

Whilst taking the Fourier transform directly twice in a row just gives you a trivial time-inversion that would be much cheaper to implement without FT, there is useful stuff that can be done by taking ...
• 1,269
Accepted

### What is the Fourier Transform of a constant signal?

I'll complete a bit the answer given in a comment above. Intuitively first, to which frequency corresponds a signal constant in time, for exemple $x(t) = 1$ $\forall t$ ? Such a signal shows no ...
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Accepted

### Is there any practical application for performing a double Fourier transform? ...or an inverse Fourier transform on a time-domain input?

"Is there any practical application?" Definitely yes, at least to check code, and bound errors. Especially for huge data or a large number of iterations "In theory, theory and practice ...

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### Why is sampling not “idempotent”?

Here is what I think is a nice pictoral way to think through this question. Sadly there is signal processing literature out there that does equate multiplication by a Dirac comb with sampling. But ...
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### What really means stochastic in field of signal processing

I never saw the second definition, but the example of SGD actually fits the first definition. SGD works with a random estimator of the gradient, and just GD is using the real gradient (calculated). To ...
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### Is sampling at double the desired reproduction frequency accurate?

This is related to 'Three points determine a circle'. (i.e. The sine wave is a circle - i.e. draw a circle in (r,theta) and transform that to x-y with the x axis being the distance travelled along the ...
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### Is sampling at double the desired reproduction frequency accurate?

No, it is not accurate in the finite real world. Note that any finite length signal has infinite support in the frequency domain, thus is not strictly bandlimited. This is one reason why sampling ...
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### What really means stochastic in field of signal processing

I wanted to chime in a little only because I think I see why someone would have given you the obviously flawed definition of sample-by-sample. Adaptive algorithms like the LMS filter are based on a ...
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