I got this idea when I was sitting in Abhilash sir’s (Signals and Systems) class last Friday. So far, he had taken us on a journey into the world of Signals and Systems on a vehicle which was the simple RC network. We had seen the response of the system to and impulse, unit step and exponential excitations (More about that later…). Now it was time to look at sinusoidal inputs, which can be expressed as a combination of complex exponentials. I’m not going into the details, but the fascinating thing is that now, the (steady state) response of the system is nothing but the fourier transform (which I now understand to be an estimate of the manner in which energy is distributed among the different frequency components in a signal) of its natural response!!! And if you changed the frequency of the input signal and plotted the amplitude of the response, that’s nothing but the frequency response, or the filter characteristics of the system.
From the equations we deduced that the RC network was a low-pass filter. It would be nice to be able to verify it, and I think it can be done easily enough using Phoenix. Just write a loop to program the waveform generator to a sine wave of varying frequencies, and measure the corresponding amplitudes (and plot!). It can be done for different networks and we can deduce which one is the best filter and so on. Though I didn’t see a function for measuring amplitudes, in the Phoenix manual, I think it can be done with a loop and minus5000_to_5000(). Got to test it as soon as I can.