How to implement Complex Exponential Function Using Matlab ?

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Muhammad Salem
Muhammad Salem 2023-11-3
评论： Star Strider 2023-11-4
Please
How can I implement the Complex Exponential Function mentioned in this equation:
X(N) =exp^(j*w1*N) + exp^(j*w2*N)
Suppose:
F =40KHZ
N=Range 1 to 20
w1: is the first angular frequency
w1=2*pi*F
w2: is the second angular frequency
w2=2*pi*F
Finally,
display the values are saved in X(N) in command window.
We apply fast fourier transform (FFT) on X(N) Then we plot the result.

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Star Strider
Star Strider 2023-11-3
Ran in:
I am not certain what you are doing or what ‘w1’ and ‘w2’ are, so using my best guess —
format longE
F = 40E+3;
N = (0:20).';
omega1 = 2*pi*F; % Guessing: 'W1'
omega2 = 4*pi*F; % Guessing: 'w2'
X = exp(1j*omega1*N) + exp(1j*omega2*N)
X =
2.000000000000000e+00 + 0.000000000000000e+00i 2.000000000000000e+00 - 1.165637649496438e-11i 2.000000000000000e+00 - 2.331275298992875e-11i 2.000000000000000e+00 - 3.496912948489312e-11i 2.000000000000000e+00 - 4.662550597985751e-11i 2.000000000000000e+00 + 2.909640830059826e-10i 2.000000000000000e+00 - 6.993825896978625e-11i 2.000000000000000e+00 - 4.308406009455551e-10i 2.000000000000000e+00 - 9.325101195971502e-11i 2.000000000000000e+00 + 2.443385770261251e-10i 2.000000000000000e+00 + 5.819281660119652e-10i 2.000000000000000e+00 - 4.774661069254125e-10i 2.000000000000000e+00 - 1.398765179395725e-10i 2.000000000000000e+00 + 1.977130710462676e-10i 2.000000000000000e+00 - 8.616812018911102e-10i 2.000000000000000e+00 - 5.240916129052701e-10i 2.000000000000000e+00 - 1.865020239194300e-10i 2.000000000000000e+00 - 1.245896296856808e-09i 2.000000000000000e+00 + 4.886771540522501e-10i 2.000000000000000e+00 - 5.707171188851276e-10i 2.000000000000000e+00 + 1.163856332023930e-09i
.
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Muhammad Salem
Muhammad Salem 2023-11-4
@Star Strider
@Walter Roberson
I am really sorry
The question has been updated. Perhaps the question contains some errors or may not be clear.
Please give me the answer again
Star Strider
Star Strider 2023-11-4
That simply requires minor tweaks to the existing code.
See the documentation on the fft function to perform the Fourier transform. There are abundant examples throughout Answers. (I wrote many of them.)
That result may not be very exciting to view, since ‘X’ is created by returning integer multiples of .

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