How to represent waveform (sum of sinusoids) in complex notation

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Nathan Kennedy 2018-1-9

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https://ww2.mathworks.cn/matlabcentral/answers/376303-how-to-represent-waveform-sum-of-sinusoids-in-complex-notation

评论： Jan 2018-1-9

采纳的回答： Jan

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Hi,

I have a sum sinusoids to make a waveform, each sinusoid has a different phase attached to it.

clear
f = (20.2 : 0.01 : 21.2)*10^9;
Fs = 5*max(f);
Ts = 1/Fs;
end_t = 0.2*10^(-6);
dt = 0 : Ts : end_t-Ts;
for a = 1:length(f)-1
    random_phase = 2*pi*rand(1,1);
    %y(a,:) = 2 * sin(2*pi .* f(a) .* dt + random_phase);
end
waveform = sum(abs(y))
plot(dt,waveform)

I need to amplify this waveform, but the amplification being applied is in the form of a vector, it has an increase amplitude (gain) component and also a phase change component.

So the waveform is amplified but also subjected to phase change at instances in time.

To do this, my original waveform must be complex so I can multiply two complex numbers together to get the amplified waveform.

How do I do get my original code in a complex form?

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Answer 1

Jan 2018-1-9

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https://ww2.mathworks.cn/matlabcentral/answers/376303-how-to-represent-waveform-sum-of-sinusoids-in-complex-notation#answer_299329

编辑：Jan 2018-1-9

在 MATLAB Online 中打开

What about:

y(f,:) = cos(2*pi .* f .* dt  + random_phase) + ...
         1i * sin(2*pi .* f .* dt  + random_phase);

Or equivalently:

y(f,:) = exp(1i * (2*pi .* f .* dt + random_phase));

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Nathan Kennedy 2018-1-9

编辑：Nathan Kennedy 2018-1-9

I had to edit my original post because I pasted in test code that wasn't working. My original post now has working code.

I tried your idea and it works, but why is the imaginary component (sin) exactly the same as the real part (cos) in your code. Can this be trimmed down?