ftt of cosine wave

Hello everyone,

I have tried to have the fft from a cosine wave. The form of the final function the place where I must have the delta are correct, but the amplitude of the delta is 10.5. The code is the following:

clc
clear all
close all
N=21;
F0=1/N;
n=[0:N-1];
s=cos(2*pi*F0*n);
S=fft(s);
fs=1/210;
Fs=[0:fs:fs*(21-1)];
stem(Fs,abs(S));

Thank you!

[Walter Roberson]

10.5 for the positive frequency + 10.5 for the negative frequency = 21 = N

[Franco Riggio]

But it has to be 0.5 because that is the fourier transform from a cosine wave. In fact, if I add another cosine with another frecuency, the fft is the deltas from both cosines, but with the same amplitude (10.5)

[Walter Roberson]

Normalize by dividing by N.

[Walter Roberson]

Franco Riggio comments to me,

Thank you, the answer was the correct one! But why do you have to normalize it? Do you have to do it everytime you want to plot it? What do I have to do if I have more than one cosine?

[Walter Roberson]

I seem to recall it is an adjustment needed when converting between continuous and the most common implementations for discrete.