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:
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!