math121a-f23:hw_8
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
math121a-f23:hw_8 [2023/10/21 05:08] pzhou |
math121a-f23:hw_8 [2026/02/21 14:41] (current) |
||
|---|---|---|---|
| Line 5: | Line 5: | ||
| Suppose you are given a function on an interval, $f(x): [0, 1] \to \R$. Such function $f(x)$ can be expressed as a sum of 'sine waves' and cosine waves and constant | Suppose you are given a function on an interval, $f(x): [0, 1] \to \R$. Such function $f(x)$ can be expressed as a sum of 'sine waves' and cosine waves and constant | ||
| - | $$ f(x) = a_0 + \sum_{n=1}^\infty a_n \cos(n \pi x) + b_n \sin(n \pi x). $$ | + | $$ f(x) = a_0 + \sum_{n=1}^\infty a_n \cos(2n \pi x) + b_n \sin(2n \pi x). $$ |
| Can you figure out a way to determine the coefficients $a_n$ and $b_n$? | Can you figure out a way to determine the coefficients $a_n$ and $b_n$? | ||
| Line 12: | Line 12: | ||
| $$ f(x) = \begin{cases} 1 & 0 < x < 1/2 \cr | $$ f(x) = \begin{cases} 1 & 0 < x < 1/2 \cr | ||
| 0 & 1/2 \leq x \leq 1 | 0 & 1/2 \leq x \leq 1 | ||
| - | \end{\cases} | + | \end{cases} |
| + | $$ | ||
| find $a_0, a_1, b_1$ and plot the truncated Fourier series | find $a_0, a_1, b_1$ and plot the truncated Fourier series | ||
| - | $$ a_0 + a_1 \cos(\pi x) + b_1 \sin(\pi x). $$ | + | $$ a_0 + a_1 \cos(2 \pi x) + b_1 \sin(2 \pi x). $$ |
| - | How does the resemble your original given function? | + | How does this resemble your original given function? |
math121a-f23/hw_8.1697864886.txt.gz · Last modified: 2026/02/21 14:44 (external edit)
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
