Learn Matlab: Sine Wave Analysis

[zxc01]

Hello.

I have recently transferred courses, and am expected to know how to use Matlab, but have never been taught before. Therefore I have been trying to go through and teach myself some of the bits I will need to know from it.

We were told we had to know how to do certain things already and I have been going through these.


Create a sine wave, calculate the FFT of the sine wave, extract the frequency of the FFT of the sine wave from the FFT data, and know what happens to the time-domain and FFT-domain of this data if the phase of the sine wave were shifted by a few degrees.


I tried with the help of the getting started guide in Matlab itself and input:-

x=0:pi/100:2*pi
y=sin(x)
plot(x,y)

y=fft(x)

And couldn't do any of the others.

Would appreciate some help.
Thank you.

 

[matonski]

I always get slighty confused about this so I wrote myself a demo program that does just this thing. It plots a sign wave and it's Fourier transform, showing spikes at just the right places.

clear all
% play with different values of fo
fo = 4;
N = 100; 
T = 2*pi;
t = linspace(0,T,N);

% the function and its fft (shifted so zero frequency occurs in the middle)
f = sin(2*pi*fo*t);
ft = fftshift(fft(f));

% frequency goes in steps 1/T
s = (-N/2+1:N/2) * 1/T;
figure(1),plot(t,f),title('f(t) versus t')
figure(2),plot(s,abs(ft)),title('fourier transform of f at s versus s')

As far as really understanding the relationship between the discrete Fourier transform and the continuous one, this lecture really cleared things up. It's lecture number 20 in an entire class on Fourier transforms. This is the class where he introduces the discrete Fourier transform. The whole class is amazing and I highly recommend it to everyone.

 

[oswaler]

Hello,

It's great that you are taking the initiative to learn Matlab on your own. It can be a very useful tool for scientific analysis and data processing.

To create a sine wave in Matlab, you can use the "sin" function. For example, if you want to create a sine wave with a frequency of 5 Hz and a duration of 1 second, you can use the following code:

t = 0:0.001:1; % time vector from 0 to 1 second with a step size of 0.001
f = 5; % frequency of the sine wave in Hz
y = sin(2*pi*f*t); % create the sine wave

To calculate the FFT of the sine wave, you can use the "fft" function. This will give you the amplitude and phase information of the different frequency components present in the signal. To extract the frequency from the FFT data, you can use the "findpeaks" function. This will give you the frequency with the highest amplitude in the FFT data.

If you shift the phase of the sine wave by a few degrees, it will affect both the time-domain and FFT-domain data. In the time-domain, the waveform will be shifted horizontally, while in the FFT-domain, the amplitude and phase information will be affected.

I would recommend going through some tutorials or online courses to learn more about Matlab and its capabilities. The official Matlab website has a lot of resources available, including tutorials and documentation. You can also find helpful videos and tutorials on YouTube.

I hope this helps. Good luck with your learning journey!