title: what is the bandwidth of a periodic signal, if fourier transformed?
body: <p>my question is if a periodic signal is fourier transformed, will the bandwidth be equal to its frequency in time domain?</p>
  
  <p>For example, if a sine wave has the frequency w<sub>c</sub>, then in frequency domain of fourier transform, it will have two impulses at -w<sub>c</sub> and +w<sub>c</sub>, right ? So the bandwidth or the highest frequency in frequency domain is supposed to be w<sub>c</sub>, same as the frequency of the original signal in time domain.</p>
  
  <p>But is this true for any periodic signal ? 
  And another thing, how can I generate fourier transform of a periodic signal? Doesn't it violate the first condition of fourier transform ?</p>
  
  <p>I need it because Nyquist theorem states that, If a continuous time signal contains no frequency components higher than B Hz, then the sampling frequency should be F<sub>S</sub>>2B. In exercise, I am given the sum of a bunch of sine sine functions and I need to calculate the minimum sampling frequency. So I need to know the highest frequency component?</p>