フーリエ変換のあとがき

電子工学まで勉強が及びました。
Apparently, a simple low pass filter can be created by connecting a capacitor and resistor in a circuit. The initial voltage drop is the difference between the point where current has not reached either the capacitor or the resistor and the point after it has flowed through the resistor, The second "output" voltage drop is between the point after the capacitor and again the point after the resistor. (note ^ characters are placeholders for display purposes).

Vi -----------------C ---------Vo
^^^^^^^^^^^^|^^^^^^^^
^^^^^^^^^^^^|^^^^^^^^
^^^^^^^^^^^^R^^^^^^^^
^^^^^^^^^^^^|^^^^^^^^
Vi-----------------------------Vo

Due to impedance, there is an effect of resistance due to the capacitor. This impedance is inversely proportional to the frequency of the signal.
The equation for the ratio of output voltage to input voltage is:
Vo/Vi = (1/wC) / ((1/wC)+R).
Thus, for higher frequencies, Vo/Vi will tend to zero, meaning that the frequency is essentially blocked. For lower frequencies, Vo/Vi will tend to one, meaning that the frequency is preserved.
Thus, after "frequency components" of the signal are identified via the Fourier transform, they can be altered by the device above (which essentially takes the product of the ith frequency component with the ith component of a square wave). Then, the inverse Fourier transform can be used to regenerate the signal with some frequencies missing (perhaps useful in compression).