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Trying to show that columns of Fourier matrix are eigenvectors

score 763 · Answer 1 · 2026-02-23 18:11:18

763

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Trying to show that columns of Fourier matrix are eigenvectors

Published on 23 Feb 2026 - 18:11

score 105 · Answer 2 · 2017-04-18 18:45:42

105

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If $y$ is the $DFT$ of a real sequence $x$ of length $n$; where $n$ is a power of two, show that $y_0$ and $y_{n/2}$ must be real.

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score 36 · Answer 3 · 2017-04-21 18:48:48

36

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102

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288

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score 369 · Answer 6 · 2017-04-29 17:22:07

369

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score 1k · Answer 7 · 2017-05-08 08:51:57

1k

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score 233 · Answer 9 · 2017-05-19 12:38:51

233

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184

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score 33 · Answer 11 · 2017-05-24 13:26:55

33

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score 512 · Answer 12 · 2017-06-08 12:16:52

512

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score 29 · Answer 13 · 2026-03-26 12:35:14

29

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score 87 · Answer 14 · 2026-03-25 07:43:43

87

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score 397 · Answer 15 · 2026-03-25 17:37:32

397

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List Question

Trying to show that columns of Fourier matrix are eigenvectors

If $y$ is the $DFT$ of a real sequence $x$ of length $n$; where $n$ is a power of two, show that $y_0$ and $y_{n/2}$ must be real.

FFT not returning period of data

Interpreting frequency spectrum of periodic probabiltiy distribution

From acceleration spectrum to velocity

Create a graph of dominant frequencies at each point in time in signal?

Using FFT to efficiently multiply multiple polynomials modulo N

Fourier transformation formula confusion

How to get the frequency of a time-domain signal with limited sample length?

Calculate Hankel Transform by Fast Fourier Transform

Why this time-frequency representation of a pure sine function with Stockwell Transform is different in the boundary?

Is group theory useful for understanding the FFT?

How do spherical harmonic degrees compare to the Fourier domain

Discorrespondence between Continous Fourier Transform and Discrete Fourier Transform

DFT implementation: relationship between number of samples and resolution of frequency

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