[SOUND] Welcome back to Linear Circuits, this is Dr. Ferri. In our previous lesson, we introduced the concept of a frequency spectrum. In this particular lesson, we will look at real signals and compute their frequency spectra. Now, this is an example of a real signal. This comes from a sensor. I took a IR sensor, which measures the intensity of light, and I brought it in a room. And I put my hand over it and then I took it off. On, off. On, off. And this is the measurements I got out of it. So when we have the high levels, that's where it showed the most amount of light. And where it's the low levels, that's where I had my hand over the sensor. What you'll see here, is right there, there's a little bit of jaggedness on the signal. And that's measurement noise. So what a typical engineer does, when faced with measurement nose like that, wants to find out where it comes from, is they look at the frequency spectrum. And say, well, is there a certain particular frequency that's in there. And if so, can I get rid of it? Could I filter it out? So let's take a look at this. So this is my raw signal data as before. And there's an instrument called a spectrum analyzer and it computes the frequency spectrum of a measured signal and plots it versus frequency. And what happens here, if we show it on a linear scale, is that the low frequency components are really large compared to the high frequency. Low frequency includes a DC component, which is fairly significant here. And then this also repeats at about four seconds. So, there's a frequency at one over four or 0.25 hertz. So 0.25 and DC components are really large. And that's why we get very large values here. And the rest of this noise part is what we call, it's down low, that's where we get the term, it's in the noise, when we talk about signals. Because we can't even see it down here. So for that reason, we oftentimes plot the frequency spectrum on a log scale. And that's where we take 20 times the log of the magnitude. And we plot that, and the unit is in decibels. Now you've probably heard of decibels before in terms of sound. They talk about rock concerts and how many decibels they are. That's where we get that term, that's how it's defined. And when we plot in decibels, we see this peak right here. And right here, is the frequency of that noise. It shows up in the log scale, but it does not show up over here in the linear scale. And that's why we tend to use log scales to show the resolution at low amplitudes. The other application that we're going to be looking at is a guitar string. Now I want to introduce harmonics here. In a guitar string we have a particular tone, the note. And in terms of harmonics the mathematical formula of it, we call that the fundamental frequency. And then a guitar string vibrates at twice that frequency, three times that frequency, and so on. And these are called harmonics. Now just to be complete here, I'm also showing a DC component, which is right here at 0 frequency. The guitar string actually doesn't have a DC component, but in general when we talk about harmonics we include that DC component. This platform is a guitar string. We have a standard commercial guitar pick up, which is very similar to the homemade guitar pickup that we saw before when we looked at inductance and applications of inductance. The homemade one was just a coiled wire around a permanent magnet. So this one uses the same principle, but it has a better resolution to it. And the guitar string is a steel guitar string. So, as you pluck the guitar string [SOUND], it vibrates inside the magnetic field induced by this guitar pickup and it causes a current. So the current flows in through these lines right here. And then we're using this data acquisition board to just record those signals. And then we'll display the signals. So again, as I pluck the string, [SOUND] I'm inducing electrical current. Now, I want to look at this electrical current on an oscilloscope. So, if I look back at my oscilloscope here, I've got this set to record from this channel. Now let me go ahead and hit the guitar string, and we'll see what it looks like. [SOUND] And you can see a signal that looks fairly periodic, and it decays over time. Let's go ahead and zoom in on this. We definitely see something that looks periodic and that's where it gives you the tone that hear you from the guitar string, but it's not a pure tone. And this particular screenshot has a a lot of jaggedness in there and it's because the resolution under which I recorded it. I'm going to change the resolution And we'll record this again. And we'll see a little bit better resolution. [SOUND] There we go. All right, so re-running this with a better resolution, let me go ahead and zoom in on it a little bit more. And we can see this is what a guitar string vibration looks like when I pluck it. If I look at this, I see definitely a fundamental frequency. From here to here is the fundamental period, that's the basic tone that you've got, the basic note, in other words. But I also see some things happening in the middle. In fact, I see a dip right here, about halfway. So I see a dip here, a dip about halfway, and a dip here. And that dip halfway corresponds to a second harmonic. So it's another frequency in there. I mean if I look at this, I see a peak right here. That's about a third of the way. That's really a third harmonic. And then we actually see a fourth harmonic here as well. So I see multiple harmonics in this signal. Now to analyze this a little bit better, it's easier to look at a dynamic spectrum analyzer. Going back to the platform here, a dynamic spectrum analyzer is accomplished by taking your recorded signal, feeding it in through a data acquisition board and then you record that signal. Now I'm going to put that instrument up here. And let's go ahead and run this. The dynamic spectrum analyzer takes that recorded signal and performs a fast Fourier transform on it in order to get the frequency spectrum. What you see plotted here is the magnitude in decibels versus frequency. And the frequency is on a linear scale, but once we put something into decibels, it is actually a log scale. Because to compute the magnitude in decibels, we take 20 times the log of the magnitude. Now what we see here, is that there's a little bit of a peak right there, and I had not yet played a note. So, it's curious to see where that peak occurs. I'm going to turn my cursor on and go ahead and slide it across to see where the peak occurs. It occurs right there. And if I look at that frequency that is 60 hertz. Well, it's very, very common to get noises at 60 hertz because this it's electromagnetic noise. And it's induced by powerlines in the room. It could be induced by vibrations from equipment, which is powered by 60 hertz powerlines. So, in this country, the line current is at 60 hertz. So we see 60 hertz signals, in noise and signals. In other countries you might have 50 hertz, and then therefore your noise will be at 50 hertz. But that peak there has nothing to do with our experiment. So we're going to ignore that 60 hertz peak in our experiment. We're just going to be looking at the peaks due to plucking this string. So if I pluck the string again. [SOUND] What I see are all of these peaks. This is the fundamental frequency that we saw in our times trace. This is the second harmonic, the third harmonic. And this case, the second harmonic is almost as strong as the first harmonic, a little bit lower. And let's go ahead and measure what that frequency is. I'm going to turn my cursor on. Slide this across. About as close as I can, it's around 440. And that's an A note. Now, what we're seeing is we've got our A note, and then we've got our higher harmonics. And that's what gives the richness of sound in most musical instruments that rely on the harmonics to give it the richness of the sound. So, in this case we've looked at the application of the frequency spectra in order to analyze the signal. We will be using this experiment later, when we go on to filtering, to say, what if we don't want to hear that second harmonic? What if we wanted to get rid of the 60 hertz signal? And so we want to use this experiment later for filtering. Basic concepts that we've covered, though, were to look at the dynamic spectrum analyzer and to look at the frequency spectrum that we get out of a real signal. To summarize the key concept, we've looked at frequency spectra of real signals. And one of the things we pointed out is that we use the log scale typically. And that's to show better resolution at low amplitudes. The other thing we introduced was the idea of harmonics, where we have a fundamental frequency and then integer multiples of that frequency. The other thing I wanted to point out is that the real spectra oftentimes has a continuum of frequencies, not just discreet frequencies. All right, thank you very much. [SOUND]
