Plotting complex sinusoid to a cosine wave

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ssmith
ssmith 2023-1-15
评论： Star Strider 2023-1-16
I have the complex exponential equation (z) and I want to adjust the plot to produce a cosine wave of amplitude of 5.0 that is shifted by 45 degrees. I have attached my code so far below. If someone could direct me to where I should make adjustments to plot a cosine wave with a = 5.0 shifted by 45 degrees that would be greatly appreciated. Thank you.
z = exp(-j*2*pi*t);
clear all; close all;
Tt = 1; % Total time
fs = 500; % Sampling frequncy
t = (0:1/fs:Tt); % Time vector
a = 5.0; % Amplitude
z = exp(-j*2*pi*t); % Complex sinusoid
plot(t,real(z),'k',t,imag(z),':k'); % Plot result
xlabel('Time (sec)', 'FontSize',14);
ylabel('y(t)','FontSize',14);

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回答（1 个）

Star Strider
Star Strider 2023-1-15
Ran in:
Add to the complex argument to shift the complex exponential result by 45° —
Tt = 1; % Total time
fs = 500; % Sampling frequncy
t = (0:1/fs:Tt); % Time vector
a = 5.0; % Amplitude
z = exp(-1j*(2*pi*t+pi/4)); % Complex sinusoid
plot(t,real(z),'k',t,imag(z),':k'); % Plot result
xlabel('Time (sec)', 'FontSize',14);
ylabel('y(t)','FontSize',14);
.
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ssmith
ssmith 2023-1-16
Oh ok, so to follow the exact phrase, your method is correct, but my 'z' also works?
Star Strider
Star Strider 2023-1-16
Not quite, since it multiplies both the real and imaginary parts of ‘z’ by ‘a’.
To be absolutely rigorous, the real and imaginary parts of ‘a’ need to be multiplied respectively by the real and imaginary parts of ‘z’.
Your Question specified that the cosine (real) part of the complex exponential function was to be multiplied by ‘a’. It just depends on how much detail (and how rigorously) you want to define this.
I leave that to your discretion.

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