List questions from fourier-analysis

Published on 15 Apr 2026 - 6:58

503

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Stuck on this integration $\int_0 ^\infty \frac{1}{1+x^2} \cos(kx) dx =\frac{\pi}{2}e^{-k}$

Published on 15 Apr 2026 - 9:25

1k

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fourier transform and principal values

Published on 12 Apr 2026 - 2:06

44

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Prove $\int_0^\infty f(t) \frac{1}{t+x} dt$ is its own Fourier cos transform if $f(t)$ is its own Fourier cos transform

Published on 15 Apr 2026 - 18:56

348

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Calculating value of integral of convolution using Fourier transform

Published on 11 Apr 2026 - 21:45

50

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Proving orthonormality of system by sum of fourier coefficients

Published on 12 Apr 2026 - 10:38

76

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Making it possible to do a Fourier transform on it: $\frac{1}{(k+w)^2(a^2 +w^2)}$

Published on 15 Apr 2026 - 18:28

590

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Entire function of exponential type $1$ bounded by $1/(1+|x|)$

Published on 13 Apr 2026 - 21:15

44

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Fourier Transform Properties Established

Published on 10 Apr 2026 - 14:27

1k

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Fourier Transform Properties - Proving

Published on 10 Apr 2026 - 20:33

37

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Show that f and fourier are in S(R)

Published on 15 Apr 2026 - 5:59

2k

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Find the Fourier Coefficients that minimize the error

Published on 14 Apr 2026 - 17:12

446

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What is the relationship between DTFT and continuous fourier transform?

Published on 10 Apr 2026 - 0:42

604

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Is the DTFT of a sampled Gaussian a positive function?

Published on 11 Apr 2026 - 0:26

1k

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How does equality in Bessel's Inequality prove an orthonormal complete sequence?

Published on 14 Apr 2026 - 5:52

List Question

Result obtained on deletion of finite number of Fourier Coefficients

Stuck on this integration $\int_0 ^\infty \frac{1}{1+x^2} \cos(kx) dx =\frac{\pi}{2}e^{-k}$

fourier transform and principal values

Prove $\int_0^\infty f(t) \frac{1}{t+x} dt$ is its own Fourier cos transform if $f(t)$ is its own Fourier cos transform

Calculating value of integral of convolution using Fourier transform

Proving orthonormality of system by sum of fourier coefficients

Making it possible to do a Fourier transform on it: $\frac{1}{(k+w)^2(a^2 +w^2)}$

Entire function of exponential type $1$ bounded by $1/(1+|x|)$

Fourier Transform Properties Established

Fourier Transform Properties - Proving

Show that f and fourier are in S(R)

Find the Fourier Coefficients that minimize the error

What is the relationship between DTFT and continuous fourier transform?

Is the DTFT of a sampled Gaussian a positive function?

How does equality in Bessel's Inequality prove an orthonormal complete sequence?

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