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# [SOLVED]Fourier transform of cosine

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#### Mustaine

##### Member level 1
Hello friends why matlab gives the magnitude fourier transform of cosine as 250.
is not it should be 1/2 according to the equation below.
thanks
--- Updated ---

this is the matlab code:
Code:
Tsample = 1/50;
t = 0:Tsample:10-Tsample;
x = cos(2*pi*10*t);
figure
plot(t,x)
xlabel('Time (seconds)')
ylabel('Amplitude')
y = fft(x);
fsample = 1/Tsample;
n = length(x);
fshift = (-n/2:n/2-1)*(fsample/n);
yshift = fftshift(y);
figure
stem(fshift,abs(yshift))
xlabel('Frequency (Hz)')
ylabel('Magnitude')
--- Updated ---

i tried to do that on simulink by changing the frequency as 1k .
type of the spectrum power and the unit is watts but i get the magnitude as 0.25.
is that value correct
also the magnitude is varied by the sample time why is that

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Last edited:

#### stenzer

Hi,

have look at the MATLAB help function, by entering "help fft" into your command window. There you will find an example how to use fft. It seems you forgot to divide your fft result by the number of samples (here n).

BR

#### Mustaine

##### Member level 1
Hi,

have look at the MATLAB help function, by entering "help fft" into your command window. There you will find an example how to use fft. It seems you forgot to divide your fft result by the number of samples (here n).

BR
thanks for your reply i actually imitate the code according the matlab website but on the website also magnitudes are very high i.e.(https://www.mathworks.com/help/matlab/math/fourier-transforms.html)
after i divide the magnitude to n it gave me the correct result
could you explain the reason of it

#### stenzer

Hi,

it depends on the "implementation" of the FFT, by means using a scaling factor or not. The picture below is from "Uderstanding Digital Signal Processing" by Richard G. Lyons and addresses this issue.

At the modaterators (e.g. @KlausST or @FvM ), I hope it is fine to post the picture of two page of a book (not available on google books). To be hornest it's long time ago I have read and agreed to the board rules. If it is not in agreement with the board rules, please delete the picture above.

BR

#### Mustaine

##### Member level 1
Hi,

it depends on the "implementation" of the FFT, by means using a scaling factor or not. The picture below is from "Uderstanding Digital Signal Processing" by Richard G. Lyons and addresses this issue.

View attachment 169320

At the modaterators (e.g. @KlausST or @FvM ), I hope it is fine to post the picture of two page of a book (not available on google books). To be hornest it's long time ago I have read and agreed to the board rules. If it is not in agreement with the board rules, please delete the picture above.

BR
thanks for the reply i also did not know that there is a issue about N samples i thought i was wrong.
thanks for the book recommendation.

#### stenzer

thanks for the book recommendation.
I like the mentioned book and I own an "analog" version. I refernced it as I knew Lyon is adressing this topic. If you do not want to spend money, I can recommend [1], which is freely accessable online, and also available in printed form.

[1] https://www.dspguide.com/pdfbook.htm

BR

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