[SOUND] Welcome back to Linear Circuits. This is Dr. Ferri. We're going to summarize this module. One of the first concepts we covered was frequency spectrum where we have a signal that I plot in time, for example voltage signal and I see there is more than one frequency in there. One of the tricks that we learned is to be able to plot the low frequency average. So in this dash line it's a low frequency average. And so that way we can see that there's a low frequency signal, we can find the amplitude here. The amplitude is 1.5. And I can plot it on the frequency spectrum, and then off of that there is a deviation which is the high frequency, and that high frequency has an amplitude off of that of about one. So in this particular frequency spectrum you see that the low frequency dominates the high frequency, and you can see it in this signal as well, the low frequency is more apparent, it's more dominant than the high frequency. Another aspect that we have, this is one of the most important things we covered in this module, is that of frequency response. If I input a sine wave into my circuit, and output a sine wave here, then, I will get a change in the amplitude and a change in the phase, but no change in the frequency. And that relationship goes back to the transfer function. The magnitude of the transfer function and the angle of the transfer function is how you relate the input and output angles and amplitudes. We also looked at the plot of this. So this is a plot of the magnitude, and of the angle versus omega, versus frequency. Now Bode Plots is just taking that frequency response, that transfer function, and taking 20 times the log of it and plotting this on the magnitude scale in decibels. Now this particular plot shows one of a second order circuit. And I can tell that by seeing that there's a resonant peak right there. One of the most important concepts that we've covered in this module is filters. And in particular we looked at lowpass filters and highpass filters. And I'm showing here just their basic characteristics. The low frequency gain, the passband, and the bandwidth here and the highpass filter, it has this general characteristic where it boosts the high frequency. And this is a passband gain. And this is passband region. And we show the corner frequency right there. Now what's more important is how it treats signals. So for example if this is my input, and this has a low frequency and a high frequency, if the low frequency is in the passband region and the high frequency is in what we call the stopband region, or over here, this is what I'm going to get as my output signal. I've diminished the high frequency, I've filtered it out. Now, if I took that same input and put it through the highpass filter, and again my corner frequency was between those two frequencies here, so the low frequency was in this region and it was attenuated. And the high frequency was in this range where it was passed through, I would get this sort of signal. So the same input to these two different circuits will give you very different outputs. For completeness sake, we also introduced to you to two other types of filters. A bandpass filter, where the passband was in a band right here. And we attenuated signals of low frequency and high frequency. Those in the middle were passed through. We also introduced you to a notch filter, which is the exact opposite. There's a region in the middle where we stop the frequencies. And so we pass through frequencies at low frequencies and frequencies at high frequencies. All right, thank you. [MUSIC]