title: FFT normalization
body: <p>I know this question has been asked ad nauseam but somehow I can't make it work properly. I created a single, sine wave of 440 Hz having  a unit amplitude. Now, after the FFT, the bin at 440 Hz has a distinct peak but the value just isn't right. I'd expect to see 0 dB since I'm dealing with a unit amplitude sine wave. Instead, the power calculated is well above 0 dB. The formula I'm using is simply</p>
  
  <pre><code>for (int i = 0; i &lt; N/2; i++) 
  {  
      mag = sqrt((Real[i]*Real[i] + Img[i]*Img[i])/(N*0.54)); //0.54 correction for a Hamming Window
  
      Mag[i] = 10 * log(mag) ;      
  }
  </code></pre>
  
  <p>I should probably point out that the total energy in the time domain is equal to the energy in the frequency domain (Parseval's theorem), so I know that my FFT routine is fine.</p>
  
  <p>Any help is much appreciated.</p>