Plotting even and odd extensions of a function

3 次查看（过去 30 天）
steven
steven 2019-3-16
评论： Star Strider 2019-3-16
What's an easy way of plotting odd or even extentions of a function on the whole real number line?
For instance, if you are given on , how can one plot the fourier series of this function for odd and even extentions.

请先登录，再回答此问题。

回答（1 个）

Star Strider
Star Strider 2019-3-16
I am not certain what you mean by ‘extensions’.
Fourier series are comprised of cosine functions (real coefficients) that are even, and sine functions (imaginary coefficients) that are odd. See the Wikipedia article on Even and odd functions (link) for an extended discussion.
  2 个评论
steven
steven 2019-3-16
This example from Desmos visualizes what I mean by odd extention. I would like to plot a simliar piecewise function on all real number line.
Star Strider
Star Strider 2019-3-16
I’m still not certain what you mean by ‘extension’.
That page illustrates the effect of adding more Fourier analysis ‘frequencies’ (with their associated coefficients) to the reconstruction of that waveform. The more terms you add, the more closely the reconstruction from the Fourier coefficients will approach the analysed waveform.
With respect to a square wave, that is very easy to demonstrate:
t = linspace(0, 3, 500);
f = sin(t(:) * [1 3 5 7 9] *2*pi) * 1./[1 3 5 7 9];
figure
plot(t, cumsum(f,2))
grid
Experiment to get the result you want.

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Fourier Analysis and Filtering 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by