Inquiry about Fourier Transform

Hello.

Hello.

According to Matlab documents regarding to Fourier Transform calculation, the code to do so is:

Ts = 1/25;

t = 0:Ts:10-Ts;

x = sin(2*pi*15*t) + sin(2*pi*20*t);

plot(t,x)

xlabel('Time (seconds)')

ylabel('Amplitude')

y = fft(x);

fs = 1/Ts;

f = (0:length(y)-1)*fs/length(y);

plot(f,abs(y))

xlabel('Frequency (Hz)')

ylabel('Magnitude')

title('Magnitude')

n = length(x);

fshift = (-n/2:n/2-1)*(fs/n);

yshift = fftshift(y);

plot(fshift,abs(yshift))

xlabel('Frequency (Hz)')

ylabel('Magnitude')

I have some inquiries:

I do not understand variable f and fshift?

• What does mean?
• Is always write it like that?
• How can I show the expression for y = fft(x)?

Answer 1

[Pratyush Roy]

Hi,

The variables f and fshift are MATLAB arrays which represent the frequency components of a signal, where the array f varies within the interval [0,Fs] and fshift varies within the interval [-Fs/2,Fs/2]. While performing fftshift, we shift the zero-frequency component to the center of the spectrum. As a result, the spectrum is now centered around zero. We can choose different variable names for them as well.

When you mention show the expression y=fft(x), I understand you want to show the values in the y-array containing the FFT values. You can either print them out using disp

disp(y)

You can also plot the magnitude using the plot function

y = fft(x);   
fs = 1/Ts; %Ts = Sampling interval 
f = (0:length(y)-1)*fs/length(y);
plot(f,abs(y))

Hope this helps!

[Angel Lozada]

Pratyush Roy

Thanks for your soon ansewer, as well for cooperation and kindness.

Regarding one of my question: Is always like that?. I mean: why f is defined as

f = (0:length(y)-1)*fs/length(y) and not as f = 0:fs/10:fs?

Regarding the question: How can I show the expression for y = fft(x)? I mean, I want to see the fourier transform function.

Regards