math121a-f23:hw_7
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math121a-f23:hw_7 [2023/10/14 08:15] pzhou |
math121a-f23:hw_7 [2026/02/21 14:41] (current) |
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| 2. Recall that if $f(x) = 1/(1+x^2)$, then its Fourier transformation is $F(p) = (1/2) e^{-|p|}$. Can you verify Parseval' | 2. Recall that if $f(x) = 1/(1+x^2)$, then its Fourier transformation is $F(p) = (1/2) e^{-|p|}$. Can you verify Parseval' | ||
| - | 3. Let $f(x) = 1$ for $x \in [0,1]$. Compute the convolution $(f\star f)(x)$. Can you plot it? What's the Fourier transformation of $f$ and $f \star f$? | + | 3. Let $f(x) = 1$ for $x \in [0,1]$. Compute the convolution $(f\star f)(x)$. Can you plot it? What's the Fourier transformation of $f$ and $f \star f$? (The one for $f$ is already done in HW6). |
math121a-f23/hw_7.1697271350.txt.gz · Last modified: 2026/02/21 14:44 (external edit)
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