energy of a signal in t and f domain

5 次查看（过去 30 天）
Ray Lee
Ray Lee 2014-12-3
评论： Ray Lee 2014-12-5
The energy of a signal is expected to be the same in t and f domain.
n = 1e4;
dx = 0.25;
x = rand(n,1) -0.5;
ex = sum(x.^2) *dx; % energy in t domain
y = fft(x);
fs = 1/dx;
df = fs/n;
ya = abs(y);
ey = sum(ya.^2) *df; % energy in f domain
but from the code, ey/ex=16, exactly the squared fs.
what's the problem?

请先登录，再回答此问题。

采纳的回答

Star Strider
Star Strider 2014-12-3
You need to normalise the fft by dividing it by the length of the signal:
y = fft(x)/length(x);
See the documentation for fft for details.
  2 个评论
Ray Lee
Ray Lee 2014-12-4
Before, I got ey/ex=16
after normalization, I got ey/ex=1.6000e-07

请先登录，再进行评论。

更多回答（1 个）

Ray Lee
Ray Lee 2014-12-5
I found the solution myself.
Normalizing spectral amplitude by fs will work.
But I don't know why to do this.

类别

在 Help Center 和 File Exchange 中查找有关 Spectral Measurements 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