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Title: Parseval’s Identity for Step Functions
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Series: Fourier Transform
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Chapter: Fourier Series
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YouTube-Title: Fourier Transform 12 | Parseval’s Identity for Step Functions
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Subtitle on GitHub: ft12_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Consider the set of $2\pi$-periodic step functions $\mathcal{S}_{2\pi \mathrm{-per}}$, constructed by linear combinations of $h_a$ functions. What is not correct?
A1: A given $g \in \mathcal{S}_{2\pi \mathrm{-per}}$ only has finitely many values.
A2: $\mathcal{S}_{2\pi \mathrm{-per}}$ forms a vector space.
A3: Every $g \in \mathcal{S}{2\pi \mathrm{-per}}$ can be written as $\sum{j =1}^m \lambda_j h_{a_j}$.
A4: A given $g \in \mathcal{S}_{2\pi \mathrm{-per}}$ is always a non-negative.
Q2: What is correct for $g \in \mathcal{S}_{2\pi \mathrm{-per}}$ and its Fourier coefficients $c_k$?
A1: $\sum\limits_{k = -\infty}^\infty c_k = g$
A2: $\sum\limits_{k = -\infty}^\infty c_k = | g |$
A3: $\sum\limits_{k = -\infty}^\infty |c_k| = | g |$
A4: $\sum\limits_{k = -\infty}^\infty |c_k|^2 = | g |^2$
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Last update: 2025-09
