Power/Amplitude Response of a system I am currently looking over filters and understand the frequency response of a system, e.g. a low-pass filter. However I am confused by the 'Power/Amplitude response' of a system as detailed in my notes below:


  Square of the amplitude response, or power response:
  
  $$|H(\omega)|^2=H(\omega)H^*(\omega)=H(\omega)H(-\omega) $$


I created a basic matlab scenario for the a low-pass filter and plotted the frequency response and the power response:



From the top graph I understand that as the frequency increases along the x-axis you get an attenuation for difference frequency components in db.
However I do not understand what the significance or intuitive value is gained by squaring the attenuation (or gain). I can see that the gain becomes more negative as frequency increases and the amplitude response increases.
So for example my 3dB cut-off point is at 1rad/s, 10^(0). This has a corresponding amplitude response value of 9. Does this mean the amplitude has decreased by a ninth? Because surely if my gain were positive my amplitude response value would also be a positive number and so the opposite cannot be true?

Any help would be greatly appreciated!

Regards

Pat
Your second plot is the square of the magnitude of the frequency response in dB, which indeed doesn't make much sense. You must use $|H(j\omega)|^2$, and not $(20\log_{10}|H(j\omega)|)^2$, as you did. Of course, $|H(j\omega)|^2$ will not give you any new information compared to $H(j\omega)$.