0:00

[SOUND] Welcome back to Linear Circuits,

Â this is Dr. Ferri.

Â In our previous lesson, we introduced the concept of a frequency spectrum.

Â In this particular lesson, we will look at real signals and

Â compute their frequency spectra.

Â 0:19

Now, this is an example of a real signal.

Â This comes from a sensor.

Â I took a IR sensor, which measures the intensity of light,

Â and I brought it in a room.

Â And I put my hand over it and then I took it off.

Â On, off.

Â On, off.

Â And this is the measurements I got out of it.

Â So when we have the high levels, that's where it showed the most amount of light.

Â And where it's the low levels, that's where I had my hand over the sensor.

Â 0:48

What you'll see here, is right there,

Â there's a little bit of jaggedness on the signal.

Â And that's measurement noise.

Â So what a typical engineer does, when faced with measurement nose like that,

Â wants to find out where it comes from, is they look at the frequency spectrum.

Â And say, well, is there a certain particular frequency that's in there.

Â And if so, can I get rid of it?

Â Could I filter it out?

Â So let's take a look at this.

Â 1:13

So this is my raw signal data as before.

Â And there's an instrument called a spectrum analyzer and it computes

Â the frequency spectrum of a measured signal and plots it versus frequency.

Â And what happens here, if we show it on a linear scale, is that

Â the low frequency components are really large compared to the high frequency.

Â Low frequency includes a DC component, which is fairly significant here.

Â 1:42

And then this also repeats at about four seconds.

Â So, there's a frequency at one over four or 0.25 hertz.

Â So 0.25 and DC components are really large.

Â And that's why we get very large values here.

Â And the rest of this noise part is what we call, it's down low,

Â that's where we get the term, it's in the noise, when we talk about signals.

Â Because we can't even see it down here.

Â 2:23

And we plot that, and the unit is in decibels.

Â Now you've probably heard of decibels before in terms of sound.

Â They talk about rock concerts and how many decibels they are.

Â That's where we get that term, that's how it's defined.

Â And when we plot in decibels, we see this peak right here.

Â And right here, is the frequency of that noise.

Â It shows up in the log scale, but it does not show up over here in the linear scale.

Â And that's why we tend to use log scales to show the resolution at low amplitudes.

Â 2:58

The other application that we're going to be looking at is a guitar string.

Â Now I want to introduce harmonics here.

Â In a guitar string we have a particular tone, the note.

Â And in terms of harmonics the mathematical formula of it,

Â we call that the fundamental frequency.

Â And then a guitar string vibrates at twice that frequency,

Â three times that frequency, and so on.

Â And these are called harmonics.

Â Now just to be complete here,

Â I'm also showing a DC component, which is right here at 0 frequency.

Â The guitar string actually doesn't have a DC component,

Â but in general when we talk about harmonics we include that DC component.

Â 3:47

We have a standard commercial guitar pick up,

Â which is very similar to the homemade guitar pickup that we saw before

Â when we looked at inductance and applications of inductance.

Â The homemade one was just a coiled wire around a permanent magnet.

Â So this one uses the same principle, but it has a better resolution to it.

Â And the guitar string is a steel guitar string.

Â So, as you pluck the guitar string [SOUND], it vibrates inside

Â the magnetic field induced by this guitar pickup and it causes a current.

Â So the current flows in through these lines right here.

Â And then we're using this data acquisition board to just record those signals.

Â And then we'll display the signals.

Â So again, as I pluck the string, [SOUND] I'm inducing electrical current.

Â 4:47

Now, I want to look at this electrical current on an oscilloscope.

Â So, if I look back at my oscilloscope here,

Â I've got this set to record from this channel.

Â Now let me go ahead and hit the guitar string, and we'll see what it looks like.

Â 5:27

We definitely see something that looks periodic and that's where it gives you

Â the tone that hear you from the guitar string, but it's not a pure tone.

Â And this particular screenshot has a a lot of jaggedness in there and

Â it's because the resolution under which I recorded it.

Â I'm going to change the resolution And we'll record this again.

Â And we'll see a little bit better resolution.

Â 5:58

[SOUND] There we go.

Â All right, so re-running this with a better resolution, let me go ahead and

Â zoom in on it a little bit more.

Â And we can see this is what a guitar string vibration looks like when I

Â pluck it.

Â If I look at this, I see definitely a fundamental frequency.

Â From here to here is the fundamental period,

Â that's the basic tone that you've got, the basic note, in other words.

Â But I also see some things happening in the middle.

Â In fact, I see a dip right here, about halfway.

Â So I see a dip here, a dip about halfway, and a dip here.

Â And that dip halfway corresponds to a second harmonic.

Â So it's another frequency in there.

Â I mean if I look at this, I see a peak right here.

Â That's about a third of the way.

Â That's really a third harmonic.

Â And then we actually see a fourth harmonic here as well.

Â So I see multiple harmonics in this signal.

Â Now to analyze this a little bit better,

Â it's easier to look at a dynamic spectrum analyzer.

Â 7:46

The dynamic spectrum analyzer takes that recorded signal and

Â performs a fast Fourier transform on it in order to get the frequency spectrum.

Â What you see plotted here is the magnitude in decibels versus frequency.

Â And the frequency is on a linear scale, but

Â once we put something into decibels, it is actually a log scale.

Â Because to compute the magnitude in decibels,

Â we take 20 times the log of the magnitude.

Â 8:19

Now what we see here, is that there's a little bit of a peak right there, and

Â I had not yet played a note.

Â So, it's curious to see where that peak occurs.

Â I'm going to turn my cursor on and go ahead and

Â slide it across to see where the peak occurs.

Â It occurs right there.

Â And if I look at that frequency that is 60 hertz.

Â Well, it's very,

Â very common to get noises at 60 hertz because this it's electromagnetic noise.

Â And it's induced by powerlines in the room.

Â It could be induced by vibrations from equipment,

Â which is powered by 60 hertz powerlines.

Â So, in this country, the line current is at 60 hertz.

Â So we see 60 hertz signals, in noise and signals.

Â In other countries you might have 50 hertz, and

Â then therefore your noise will be at 50 hertz.

Â But that peak there has nothing to do with our experiment.

Â So we're going to ignore that 60 hertz peak in our experiment.

Â We're just going to be looking at the peaks due to plucking this string.

Â So if I pluck the string again.

Â [SOUND] What I see are all of these peaks.

Â This is the fundamental frequency that we saw in our times trace.

Â This is the second harmonic, the third harmonic.

Â And this case, the second harmonic is almost as strong as the first harmonic,

Â a little bit lower.

Â And let's go ahead and measure what that frequency is.

Â I'm going to turn my cursor on.

Â 10:10

Now, what we're seeing is we've got our A note, and

Â then we've got our higher harmonics.

Â And that's what gives the richness of sound in most musical instruments

Â that rely on the harmonics to give it the richness of the sound.

Â 10:23

So, in this case we've looked at the application

Â of the frequency spectra in order to analyze the signal.

Â We will be using this experiment later, when we go on to filtering,

Â to say, what if we don't want to hear that second harmonic?

Â What if we wanted to get rid of the 60 hertz signal?

Â 10:52

Basic concepts that we've covered, though, were to look at the dynamic spectrum

Â analyzer and to look at the frequency spectrum that we get out of a real signal.

Â To summarize the key concept, we've looked at frequency spectra of real signals.

Â And one of the things we pointed out is that we use the log scale typically.

Â And that's to show better resolution at low amplitudes.

Â The other thing we introduced was the idea of harmonics,

Â where we have a fundamental frequency and then integer multiples of that frequency.

Â The other thing I wanted to point out is that the real spectra

Â oftentimes has a continuum of frequencies, not just discreet frequencies.

Â