>> FFT example
Tony: Hi.
This is Tony and Ian.
Ian: We're hiding out here at a coffee shop.
They don't know we're here, but we'll be done quickly.
Tony: What are we going to talk about here?
Ian: We're going to show you one more demonstration of the Fast Fourier Transform---the FFT.
Tony: Yeah, because in our last video, we promised a demo.
Ian: We did, and we want to deliver.
So we've got some footage from a live demo we did last year at the ACCESS Academy, talking
about instruments.
Tony: That was a lot of fun.
Instruments!
When we talk about instruments, I've got an instrument: a piano.
Ian: Yep, that's actually the kind of instrument we're talking about: measurement instruments
together with musical instruments.
Tony: Oh, and how they work together, and how you can see musical stuff on this.
Ian: Exactly, because the different sounds that you hear correspond to the different
shapes that you see, and we found that a useful way to introduce the concept of the frequency
transform to a new audience.
Tony: That sounds great.
Ian: All right, let's check it out.
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Ian: We mentioned music a second ago.
We're going to do another oscilloscope demo now.
Tony: This is really cool: another demo.
Ian: A sound---before you hear it---coming out of a band on stage was at some point an
electrical signal in a wire.
And so of course we can see those same kinds of things on the oscilloscope.
And the shape of what we see on the screen is related to the type of sound that we hear.
Imagine drawing a graph of every key on the keyboard.
So now our X axis isn't time any more.
We're drawing a graph, but now the X axis is pitch.
And you guys remember what the alternative word for pitch was from a few pages ago?
Student: Frequency.
Ian: Frequency.
Yep, exactly.
So now the X axis is frequency.
And if any note is not being played right now, it's going to have a very, very low voltage.
And any note that is being played will have just one little spike there.
Tony: Imagine this being the sine wave that we were showing you earlier.
And now what we're doing is---we're turning this thing on an angle like this.
Imagine looking down this way, and you're seeing the spikes in this form here.
It's taking the same signal, but we're just looking at it a little differently.
Ian: And so this operation is called a frequency transform, and the oscilloscope can do it.
So, can we do the A440 again?
We'll turn on Math and hit FFT, which stands for Fast Fourier Transform.
And it's not a perfect sine wave, so there's other crud in here.
But you can see there's one big spike here.
And if she adds another "A" an octave above that one, you'll see two big spikes here.
And these are at 440 Hz and 880 Hz.
I could probably---
Tony: Could you turn that down a little?
Ian: Yes.
Tony: This is nice about the oscilloscope: you can see both views at the same time.
We're just going to show you the one that we're talking about.
Ian: So now, can we try playing, let's say a "C" chord?
So, we see these three main spikes.
They're really, really close together---in fact, they're too close together for the instrument
to tell them apart unless we change some other settings.
So let's go back to the single note again, the A440: this nice one big spike.
What happens if we change instruments?
What do you guys think will happen here in the frequency view?
Student: I think there'll be a more definite spike and smaller secondary spikes.
Ian: So this one's a square wave, and I'm going to turn on this so we can see.
There's what it---can we hit that one more time?---there's the square wave, and I'll
turn it back off.
We can actually see that main spike is still there, but these other spikes have actually
gotten a little bit taller.
And there's a really, really strange reason for that.
You can think of any shape in there as a bunch of different sine waves added together.
So this gets right back to that question you were asking about: is there a way to mix different
signals together---
Student: It's the same result.
Ian: ---to get a more complicated one, right.
And if you build out of sine waves, there's exactly one way to do it.
If we took this sine wave, and added to it something like
this sine wave, we'd get (this).
So now, we'll add another one that's even shorter and wigglier: smaller voltage and
higher frequency.
So now we'll get something like (this).
And you can see how we're getting---the more of these we add in, the closer and closer
we get to a square wave.
So it works both ways.
You could think of being able to break a really complicated signal down into these little
pieces.
Or you could think of a way to take lots of little sine waves and build a really complicated
signal out of it.
And another way of thinking about the frequency view is---
Tony: This is what I thought was really interesting.
Ian: What if you had a signal at 94,700,000?
What if you had a radio signal that was repeating at 94,700,000 times per second---in other
words, if it was 94.7 MHz?
And then you might have another one up here at---
Tony: 107.5.
Ian: 107,500,000.
Does anyone recognize these numbers?
Student: Those are what the actual radio stations are called, like 107.5.
Ian: Exactly.
These are the frequencies that their main transmitter is transmitting at, and if we
had the right kind of antenna and a fast enough oscilloscope, we could actually draw this
same kind of orange graph of radio stations, and we'd see them all transmitting.
Tony: So, you guys understand, when you go into your radio and you put in your favorite
channel, it's actually finding that frequency.
And this thing can capture it and find out exactly if it's right or not.
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Tony: That's it.
Our video's over.
Ian: So, for more information about the Fast Fourier Transform, go to tektronix.com/fft-basics.
Tony: All right.
Ian: Bye, everybody.
Tony: Cheers.