Two-side spectrum in Matlab

Question

Hoang 2013-11-3

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/104751-two-side-spectrum-in-matlab

评论： Joao Nizer 2021-7-2

Dear my colleagues, I am a new user of Matlab. Now, I have a signal like x(t) = A1*sin(2*pi*f1*t) + A2*sin(-2*pi*f2*t), where f1, f2>0. Could anyone please show me whether I could obtain the spectrum of x in which frequency f2 is present only as a negative frequency of two-side spectrum (normally, f2 will appear in both sides of Matlab's FFT)?

Thank you very much.

Lomath.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Wayne King 2013-11-3

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/104751-two-side-spectrum-in-matlab#answer_114002

编辑：Wayne King 2013-11-3

在 MATLAB Online 中打开

Youssef is correct. Why do you think that f2 will only show up as a "negative" frequency.

sin() is an odd function so sin(-t) = -sin(t)

Accordingly, your signal is equal to

 Fs=40;
 Ts=1/Fs;
 t=0:Ts:10-Ts;
 f1=4; f2=15;
 y=sin(2*pi*t*f1)-sin(2*pi*t*f2);

If you really want components only occurring on one side, your signal must be complex-valued. Here is an example with complex exponentials.

Fs = 40; 
Ts=1/Fs;
t=0:Ts:10-Ts;  
f1 = 4; f2 = -15;
y = exp(1i*2*pi*f1*t)+exp(1i*2*pi*f2*t);
ydft = fftshift(fft(y));
df = Fs/length(y);
freqvec = -Fs/2+df:df:Fs/2;
plot(freqvec,abs(ydft))
xlabel('Hz');

2 个评论
显示无隐藏无

Hoang 2013-11-3

Thanks. Sorry for the poor example. It is great if you could give me another example, pls. In my knowledge, function x = A1*cos(2*pi*f1*t)+ A2*cos(2*pi*f2*t), where f1>0, f2<0, can be used to express a rotating signal where the first term rotates in forward direction and the other rotates in backward direction. Can it be analyzed in some ways to separate f1 and f2, pls?

Joao Nizer 2021-7-2

在 MATLAB Online 中打开

freqvec = -Fs/2+df:df:Fs/2;

should be

freqvec = -Fs/2:df:Fs/2-df;

According to https://www.mathworks.com/help/matlab/math/fourier-transforms.html

请先登录，再进行评论。

Answer 2

Youssef Khmou 2013-11-3

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/104751-two-side-spectrum-in-matlab#answer_113999

在 MATLAB Online 中打开

You can start by many tutorials, each offers a different approach to the DFT problem, in terms of resolution and amplitude estimation, i wrote a 2 sided example for you , verify it :

 Fs=40;
Ts=1/Fs;
t=0:Ts:10-Ts;
f1=4;f2=15;
y=sin(2*pi*t*f1)+sin(2*pi*t*f2);
N=length(y);
F=fft(y);
fr=(-N/2:N/2-1)*Fs/(N);
figure, plot(fr,abs(F))
xlabel(' frequency Hz')