fourier transform of sine wave help

hi everyone,

i have this simple code of a wave in time domain and frequency domain.

can someone pls help me understand this line ???

ff = Fs*(-0.5:1/length(t):0.5-1/length(t));    <-----------

thanks !

the code :

f0 = 10; 
Fs = 10*f0; 
t = 0:1/Fs:1; 
x = cos(2*pi*f0*t);

X = abs(fftshift(fft(x))); 
ff = Fs*(-0.5:1/length(t):0.5-1/length(t)); 

plot(t,x);

plot(ff,X);

Answer 1

[Star Strider]

It is coding for a two-sided (symmetric) Fourier series of the signal created in x. That is in keeping with the use of the fftshift function to define ‘X’.

[yuvi]

Thanks Star Strider for your answer !

I need to understand this line particularly.

What is the meaning of 0.5 and -0.5 and length of t....

Thanks !

[Star Strider]

My pleasure!

Putting this in context, ‘Fs’ is 100, ‘t’ goes from 0 to 1 in increments of 0.01 with a length of 101. The 0.5 (actually Fs*0.5) defines ‘ff’ to go from -50 to +50 in increments of 1/101.