List questions from fourier-series

Published on 12 Apr 2026 - 2:15

78

Views

Prove that the function $\xi\in R \mapsto {e^{i\cdot \xi\cdot λ}-1\over i\cdot \xi}-λ$ is $C^{\infty}$

Published on 12 Apr 2026 - 9:59

92

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Proving that a trigonometric sum is in $L^2$

Published on 24 May 2015 - 19:11

635

Views

Fourier Series Even Extension

Published on 12 Apr 2026 - 9:18

38

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Fourier Analysis Help - $\mathcal L^2$

Published on 12 Apr 2026 - 22:40

56

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Is there any mistake? Proof related to the Poisson summation formula.

Published on 11 Apr 2026 - 16:20

81

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Reference on Gibbs phenomenon

Published on 09 Apr 2026 - 9:22

517

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Difficult Fourier transform exercise

Published on 10 Apr 2026 - 7:59

63

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If $f \in L^2 \cap C_c$ then $\sum_{n \in \mathbb{Z}}|\hat{f}(\xi+2\pi n)|^2 = a_0+...a_n \cos(2 \pi n \xi)$

Published on 25 May 2015 - 21:32

313

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Proving Inverse DFT

Published on 26 May 2015 - 21:31

178

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Fourier synthesis of periodic signals

Published on 08 Apr 2026 - 17:39

184

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Finding the particular solution of a pde.

Published on 10 Apr 2026 - 21:50

442

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On converting from real to complex Fourier series

Published on 12 Apr 2026 - 20:04

56

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Obtaining $\sum_{n=1}^{\infty} a^n \cos{(n\theta)} = \frac{a \cos{\theta}-a^2}{1-2a\cos{\theta}+a^2}$

Published on 28 May 2015 - 18:05

20.3k

Views

Is Fourier series always used for periodic signals and Fourier transform for aperiodic signals only?

Published on 12 Apr 2026 - 14:23

List Question

Solving differential equation with Fourier-series-inhomogenity

Prove that the function $\xi\in R \mapsto {e^{i\cdot \xi\cdot λ}-1\over i\cdot \xi}-λ$ is $C^{\infty}$

Proving that a trigonometric sum is in $L^2$

Fourier Series Even Extension

Fourier Analysis Help - $\mathcal L^2$

Is there any mistake? Proof related to the Poisson summation formula.

Reference on Gibbs phenomenon

Difficult Fourier transform exercise

If $f \in L^2 \cap C_c$ then $\sum_{n \in \mathbb{Z}}|\hat{f}(\xi+2\pi n)|^2 = a_0+...a_n \cos(2 \pi n \xi)$

Proving Inverse DFT

Fourier synthesis of periodic signals

Finding the particular solution of a pde.

On converting from real to complex Fourier series

Obtaining $\sum_{n=1}^{\infty} a^n \cos{(n\theta)} = \frac{a \cos{\theta}-a^2}{1-2a\cos{\theta}+a^2}$

Is Fourier series always used for periodic signals and Fourier transform for aperiodic signals only?

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