Why do my amplitude become wrong when I vary the frequency from int to double?

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Nina 2013-2-19

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/64127-why-do-my-amplitude-become-wrong-when-i-vary-the-frequency-from-int-to-double

So I started with this code:

    A = 10;
    B= 17.6;
    C=2;
    D=11.2;
    phi1 = 2;
    phi2 = 5;
    phi3 = 1;
    phi4 = 0;
    Fs = 100;
    t = 0:1/Fs:1-1/Fs;
        x=A*sin(2*pi*10*t+phi1)+B*cos(2*pi*5*t+phi2)+C*sin(2*pi*2*t+phi3)+D*cos(2*pi*t+phi4);
        xdft = fft(x);
         magnitude = 2* abs(xdft)/length(x)
         phase     = angle(2* max((xdft))/length(x))
And that gave me all the amplitudes exactly. However when say I change the first frequency from A*sin(2*pi*10*t+phi1) to A*sin(2*pi*10.5*t+phi1), it goes crazy and give me weird output... what am I doing wrong?
Thank you

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Answer 1

Wayne King 2013-2-19

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https://ww2.mathworks.cn/matlabcentral/answers/64127-why-do-my-amplitude-become-wrong-when-i-vary-the-frequency-from-int-to-double#answer_75723

It does not go "crazy", it only gets the amplitude wrong for the frequency f = 10.5 and this is problem I explained to you in the other post. 10.5 does not correspond to a DFT bin.

See

https://www.mathworks.com/help/signal/ug/amplitude-estimation-and-zero-padding.html

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Nina 2013-2-19

Thank Wayne, I guess I am still trying to understand what is going on...basically, every time I change my frequencies, I need to make sure they fall into appropriate bins?

Nina 2013-2-19