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Title: Example for Fourier Transform
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Series: Fourier Transform
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Chapter: Continuous Fourier Transform
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YouTube-Title: Fourier Transform 25 | Example for Fourier Transform
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Subtitle on GitHub: ft25_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $f: \mathbb{R} \rightarrow \mathbb{C}$ be the indicator function of the interval $[-1,1]$. What is not correct for the Fourier transform $\hat{f}$?
A1: $\hat{f}(x) = \sqrt{ \frac{2}{ \pi } } \mathrm{sinc}(x)$
A2: $\hat{f} \notin L^1$
A3: $\lim_{\lambda \rightarrow \infty } \int_{-\lambda}^{\lambda} \hat{f}(p) dp < \infty $
A4: $\hat{f}$ is continuous with $\hat{f} \xrightarrow{p \to \infty} = 1$.
Q2: Let $f: \mathbb{R} \rightarrow \mathbb{C}$ be the indicator function of the interval $[0,\delta]$. What is correct for the Fourier transform $\hat{f}$?
A1: $\hat{f}(x) = \frac{1}{\sqrt{2 \pi}} \frac{1}{- i p } e^{- i p \delta} $
A2: $\hat{f}(x) = \frac{1}{\sqrt{2 \pi}} \frac{1}{ p } e^{ i p \delta} $
A3: $\hat{f}(x) = \frac{1}{\sqrt{2 \pi}} \frac{1}{ -p } e^{ i p \delta} $
A4: $\hat{f}(x) = \frac{1}{\sqrt{2 \pi}} \frac{1}{ i p } e^{ -i p \delta} $
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Date of video: 2025-05-14
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Last update: 2025-09
