Discrete Fourier series problem

Question

Gabriel Maia 2019-6-14

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评论： Muna Awajan 2020-5-1

Hi

I need to plot y[n]=y=1+cos(2*pi*n/N+pi/2) in discrete time and plot the calculate the Fourier coefficients in dicrete time and plot it. But i don't have the period N. How can I do this in Matlab?

Here is the code I tried to do, but it's incomplete so far.

clear
clc
N=??;    %Feriod
n=0:1:??;   %Discrete Time
y=1+cos(2*pi*n/N+pi/2);   %Discrete function
subplot(2,1,1);
stem(n,y)   %Plot discrete function
FourierCoef = fft(y);   %Fourier series function
subplot(2,1,2);
stem(n,real(FourierCoef),'k');  %Plot Fourier real coefficients

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Answer 1

James Browne 2019-6-15

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Greetings,

Are you sure that you have the right general equation for y? The function looks odd to me, when I consider the general form of the cosine function:

y = offset + amplitude*cos( angularVelocity * time + phaseShift )

For the above case, your parameters would be:

offset = 1

amplitude = 1

angularVelocity = 2*pi (radians/sec)

time = n

phaseShift = pi/2 (radians)

period = (2*pi) / (angularVelocity)

= (2*pi) / (2*pi rad/sec)

= 1 second

Ther period should not appear in the cosine function (at least I have never seen it in that configuration). Additionally, your process for evaluation the FFT of the signal is wrong. It is actually quite tricky to use the FFT function, however the MATLAB help page has some good examples, found here:

https://www.mathworks.com/help/matlab/ref/fft.html

Additionally, I often refer to this youtube video when using FFT in MATLAB. The video is old and the user interface looks very different than modern versions of MATLAB but the syntax is the same:

https://www.youtube.com/watch?v=dM1y6ZfQkDU

Hope this helps. Cheers~

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James Browne 2019-6-15

编辑：James Browne 2019-6-15

Correct, and the fast Forier transform is the frequency, amplitude and angle information of all of the coefficients in the disctrete Fourier seriese......so once you look at the FFT results and pick out the dominant signal data, you can use ifft() to transform that data back into a time domain signal, pretty sure the youtube video that I sent you the link for, covers that.

Muna Awajan 2020-5-1