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PROFESSOR: Well, today, we have
a chance to put away the
equations and have some fun.
With me is Professor Sandy Hill
from the University of
Massachusetts at Amherst.
And Sandy, maybe you could just
give us a quick tour of
what we have here.
SANDY HILL: OK.
We'll be dealing with about
four instruments today.
Two of them generate signals,
and two of them display and
analyze signals.
The first, and perhaps simplest,
is simply an RC
audio generator, that will put
out a variety wave shapes.
And we'll look at that
in a moment.
Over to the right is a device
that will allow us to study
amplitude modulation and the
various flavors of it.
Down below is a standard
oscilloscope to look at the
signals in the time domain so
we can see their shape.
And then, finally the spectrum
analyzer will analyze the
signal into its Fourier
components.
And we'll display those, so you
get to see the spectral
content of a signal.
PROFESSOR: Now, we'll be seeing
all of these in a fair
amount of detail as we go
through the demonstrations.
But maybe we can begin just
with the signal generator.
SANDY HILL: OK, let's
look quickly at the
various buttons involved.
There's a lot of flexibility
with this device.
The top three buttons here allow
us to change from one
simple wave form to another one,
a sine wave, a triangle
wave, a square wave.
And right below it is a button
that will allow us to change
the size of the signal.
Moving over towards the left,
we can change the DC offset
which varies the signal,
the level upon
which the signal rides.
PROFESSOR: And we'll be using
that actually when we
demonstrate amplitude
modulation.
SANDY HILL: That's right And
then finally, there's a way of
changing the frequency of the
signal, either changing it by
a factor of 10 or a vernier
adjustment, if you want very
specific adjustments, very
delicate changes.
PROFESSOR: OK.
So maybe we can just vary some
of this and see what a little
bit of it looks like.
SANDY HILL: All right.
What we have displayed at this
point is the effect of pushing
the sine wave button.
And so displayed down here
is a 500 Hertz sine wave.
In fact, let's listen to that.
PROFESSOR: Great.
SANDY HILL: And the scope is
said to have one millisecond
for each division here.
By varying the amplitude
knob can make the sine
wave smaller or larger.
The ear isn't too sensitive
to that.
By changing the DC offset,
it simply rides
on a different level.
It's like putting a
battery in series.
And changing the frequency,
you get a very perceptible
change, a lower frequency.
It takes longer to sweep
through a period.
Higher frequency, it takes
a shorter amount of time.
And also, we can change the wave
shape itself from a sine
wave to a triangle wave--
and you notice that has
a richer sound to it--
and then finally to a square
wave, which is an even
brighter sound.
PROFESSOR: And actually, as you
realize from the previous
lectures, with the triangle and
square wave with the same
fundamental as the sine wave,
the richness comes in because
of the higher harmonics in the
Fourier series representation.
OK, well let's go back
to the sine wave.
And we'll use that to take
a closer look at
the spectrum analyzer.
SANDY HILL: OK.
PROFESSOR: We'll look at a block
diagram of the spectrum
analyzer shortly, but first
let's just look at a few quick
things to get a feel for it.
We have, of course,
the time domain
display of the sine wave.
And the spectrum analyzer gives
us a frequency domain
analysis and display.
And the vertical axis
is the amplitude.
The horizontal axis
is frequency.
And as it's set currently, the
frequency axis goes from DC--
zero--
up to 2 kilohertz.
And that, of course,
can be varied on
the spectrum analyzer.
And since we have a sine wave
input, we get, as we would
expect, a line spectrum,
corresponding to the frequency
of the sine wave.
Now, in fact, we can measure
that frequency because the
spectrum analyzer has a cursor
associated with it, which I've
just enabled.
And this line is the
cursor line.
There is a read out for the
frequency and a read out for
the amplitude.
And let's position
the cursor on the
frequency of the sine wave.
And we're getting close.
And there we are at the
frequency of the sine wave.
And we can read out, in fact,
that it's 500 cycles.
And this is the amplitude.
And, of course, you could verify
the frequency also in
the time domain display,
simply by measuring the
frequency or the period.
SANDY HILL: This is set at
still one millisecond per
centimeter.
So that is 500 Hertz.
PROFESSOR: OK.
Well now maybe what we can
do is vary the frequency.
Let's vary the frequency of
the sine wave generator.
Maybe also listen to it?
SANDY HILL: I'll turn
on the tone.
Yep.
OK, I'll make the frequency
higher.
And you'll see a
correspondence in the time domain.
The frequency clearly goes up,
and that line of the spectrum
also migrates up away
from the cursor.
PROFESSOR: OK, and let me just
point out again that this is
the cursor line.
This isn't the spectra line.
And this is the frequency
content of the sine wave.
SANDY HILL: We can also change
the amplitude of that line by
making the sine wave
itself smaller.
And you notice the intensity
of it goes--
PROFESSOR: While you do that,
let me just position the
cursor if I can on
the sine wave.
And now as you vary the
amplitude, we should, in fact,
see this vary.
SANDY HILL: Well,
that's right.
PROFESSOR: OK.
Now as Sandy varied the
frequency, he did it slowly
and we saw the line move
as a single line.
Maybe now, Sandy, you
could vary the
frequency more rapidly.
And what will happen is that, in
fact, what we'll get if I--
SANDY HILL: There'll be
a spreading as we go--
PROFESSOR: Let me turn
the cursor off.
And what we'll see is a
spreading of the line, so that
the frequency content
is richer.
And, in fact, the analysis of
this is considerably more
complicated.
It corresponds to frequency
modulation, where Sandy is now
the modulating signal.
SANDY HILL: That's right.
PROFESSOR: And we won't really
be going into issues of
frequency modulation in any
more detail in this
demonstration.
SANDY HILL: Right.
PROFESSOR: OK, well now let's
go to the overhead projector
and take a look at a
block diagram of
the spectrum analyzer.
The specific spectrum analyzer
that we're using in the
demonstration is made by
Rockland Systems, referred to
as the Rockland Systems
Model FFT 512.
And basically, the idea is to
sample the incoming wave form,
convert that into digital form,
and then the spectrum,
in fact, is computed digitally
using a microprocessor.
So the overall system block
diagram first consists of a
system which is a
low pass filter.
And this low pass filter is
used in advance of the
sampling process to basically
reduce the artifacts that are
introduced due to sampling.
And although we haven't talked
yet about sampling and the
associated artifacts, basically,
as we'll see in the
upcoming lectures, in order to
sample a wave form and convert
it into digital form, it
requires that the wave form
first be low pass filtered.
So this low pass filter is
referred to-- and will be in
later lectures--
as an anti-aliasing filter.
And this low pass filtered wave
form is then converted to
a sequence.
And so a sequence is generated
for which the sequence values
are simply samples of the
low pass filtered input.
This low pass filtered
input is then put
into digital memory.
Basically, a time block of it
is put into digital memory,
and so that's what we
have down here.
Here is the sequence.
The sequence is put into
digital memory.
And then an arithmetic processor
computes for the
samples in this memory.
It computes the Fourier
transform or the spectrum.
And after the spectrum is
computed and put either into
the same or a different memory,
that is then put
through a conversion process
back to a continuous time
signal, and finally, put out on
the display that we've been
seeing in the demonstration.
And so this is just indicative
of the display.
So basically, the idea then
is that the input
wave form comes in.
It's filtered and sampled and
captured on a block basis, put
into a digital memory, and then,
a digital computer or
microprocessor computes
the Fourier transform.
And then that Fourier transform
is what we see on
the display.
So what we're computing, of
course, are samples of the
Fourier transform.
And so, for example, if the
input-- let's say--
was a rectangular pulse whose
Fourier transform is of the
form of a sine(x) over x
function, what we would, in
fact, see on the display are
samples of that at discrete
frequencies.
Or if as we have an input which
is a square wave, what
will generate through the
spectrum analyzer are the
Fourier series coefficients or
equivalently, the harmonics
associated with the
square wave.
OK, well, let's now go back to
the equipment and look at the
spectrum analyzer.
We'll look at the square wave
through the spectrum analyzer
shortly, but first what we have
is what we saw before,
which is the sine wave.
And just to point out, again,
the fact that the sine wave
spectrum, of course, is just a
single line corresponding to
the fundamental frequency.
And here we have a frequency
scale now that goes from 0 to
5 kilohertz.
And this is then the 500
cycle sine wave.
And, in fact, we can flip the
cursor on and I happen to just
magically have it positioned
correctly.
And we see that it's a
500 cycle sine wave.
SANDY HILL: Might be
interesting, Al, to go and
look at a richer set of signals,
such as the triangle
wave and the square wave--
things that are conveniently
on the signal generator
itself.
I'll switch over to
a square wave now.
And what you see is
all the harmonics
coming up, being displayed.
PROFESSOR: OK, it's actually
interesting to point out, I
think, that the square wave,
as we know, is an
odd harmonic function.
And so, in fact, the even
harmonics are missing in the
square wave.
So this is the fundamental.
This is the third harmonic,
fifth harmonic, et cetera.
And then the amplitude of
the square wave decays
proportional to 1 over f, which
is the kind of analysis
that we've gone through in
looking at Fourier series.
SANDY HILL: Right, and if we
switch to the triangle wave,
instead of their decaying as 1
over f, the harmonics decay as
1 over f squared.
And you see they drop off
much more quickly.
PROFESSOR: And again,
of course, it's an
odd harmonic signal.
And so the even numbered
harmonics are missing.
And maybe just to kind of
emphasize the point, we can
show the sine wave again and
the square wave again.
SANDY HILL: We'll go through
from the most bland to the
richer to the richest.
PROFESSOR: OK, and it's
really kind of
interesting and dramatic--
SANDY HILL: It's
fun to do that.
PROFESSOR: --to see the
harmonics pop in.
SANDY HILL: While we're at the
square wave, let me fiddle
with the frequency of the square
wave, and we can see
the duality of the time
and frequency domains.
That is, as you compress things
in the time domain,
such as this, going to a higher
frequency square wave,
the harmonics wonder further
away from each other.
SANDY HILL: So this is
the fundamental.
The second harmonic
is missing.
This is the third harmonic.
And of course, the fifth.
SANDY HILL: And as we take this
to an extreme by going to
very low repetition rate
square waves, all those
harmonics come scurrying in and
cluster together near DC.
PROFESSOR: Kind of fun with
Fourier transforms.
Well, speaking of time and
frequency scaling, recall that
we had demonstrated time and
frequency scaling previously
with the glockenspiel.
And what we had done there was
to record a particular
glockenspiel note, and
then we played that
back at half speed.
And what we had done in that
case is expanded things in
time, consequently compress
them in frequency.
And so, comparing that with a
note an octave lower than we
saw that, in fact, the
time scaling had led
to a frequency scaling.
And then we also played the same
note back at twice speed.
And in that case, the
frequencies were all scaled up
by a factor of 2.
And again, we illustrated that
by comparing with the
glockenspiel note a
full octave up.
Now when we did that, we didn't
actually look at the
time wave forms or spectra.
And having the equipment that we
have here gives us kind of
a nice opportunity to do that.
So what I have is the tape that
we had originally made of
the glockenspiel, the original
note that we recorded.
And what we'll do is look at the
spectrum of that, and then
compare that spectrum when we
play the tape at half speed
and also play it
at twice speed.
So let's play the tape.
And what we have is the
glockenspiel right now
displayed on a frequency scale
from 0 to 5 kilohertz.
Let's just change that to
zero to 10 kilohertz.
So here is this spectrum.
Over here we have the
time wave form.
And here is then the first
spectral line, and we can see
where that is by setting
up the cursor.
And magically, once again, I
have the cursor positioned at
just the right spot.
The first spectral line
is at 1.775 kilohertz.
And so this is the spectrum
then of the original
glockenspiel note.
All right.
Let's stop the tape
and rewind it.
And now what we want to do is
play that back at half speed.
Played at half speed,
the frequencies
should be scaled down.
And, in particular then the
first spectra line should be
at a lower frequency.
So let's play that now.
SANDY HILL: There are really
very complicated signals,
aren't they?
PROFESSOR: They really are.
Here we have the first
spectral line.
And we can compare that with the
first spectral line that
we had before which was
at 1.775 kilohertz.
And, once again, you see that
the time wave form over here
has been scaled by
a factor of 2.
So, once again, we see that
time and frequency scaling
really works.
Incidentally as Sandy pointed
out, and rightfully so, the
glockenspiel really is a pretty
complicated signal, as
a graduate student and I found
out when we were preparing the
original glockenspiel demo.
SANDY HILL: Speaking of
complicated signals, one of my
favorites is to look
at speech.
I set this up so that what's
coming into my microphone is
indeed what you're going to
see on the two screens.
The telephone company thinks of
speech, basically in terms
of bandwidth, that it extends
from about 300
Hertz to 3,300 Hertz.
But, as we'll see in the
spectrum analyzer, there's a
lot of leakage outside
of that.
The telephone company just
filters out everything outside
of that and things of that
as a speech signal.
So it doesn't have the high
fidelity that you might have
on high fire equipment.
As we look at the scope, again,
the time wave form is
extremely complicated, seems to
have some periodicities in
it, although they're
short-lived, and then it goes
on to some other
periodic chunk.
And over in the frequency
domain, you can see as we
extend from 0 to 10 kilohertz,
that as I speak, there are
trenchants that have spectral
content in them, covering that
entire band.
I can try some simpler
signals.
A whistle is almost a sinusoid,
but as you'll see
isn't terribly sinusoidal.
[HIGH-PITCHED WHISTLE]
That's the best I can do.
I can sing, a little bit
embarrassedly, a B,
[HIGH-PITCHED]
Boo, and things like that.
PROFESSOR: They don't
ask me to, Sandy.
SANDY HILL: And then different
vowel sounds have a lot of
energy in, like the letter A.
(SUNG) A. Whereas some of the
others are very impulsive,
like--
[HISSING]
Or puh and tuh.
And it's a little hard to grab
them at the right time.
But what's fascinating is just
to stare at equipment like
this and try different speech
sounds, and you begin to get
sort of a sense of the
complicated nature of them.
PROFESSOR: OK, well that's a
look at some spectra signals.
And now what we'd like to focus
on is the modulator and
talk a little bit about
modulation and demodulation
and demonstrate it.
And let's begin that by first
taking a look at a block
diagram of the modulator
system.
Well, as we've discussed in a
previous lecture, amplitude
modulation basically consists of
multiplying the modulating
signal by an appropriate
carrier, illustrated here, as
we've seen previously, for the
case of a sinusoidal carrier.
And then, specifically for
sinusoidal amplitude
modulation, we may or may not
inject some carrier signal--
A times the carrier.
Or equivalently, if we look at
the modulated output, the
injection of the carrier is
equivalent, mathematically, to
simply adding a DC offset
or a constant to
the modulating signal.
And, as you recall when we
talked about this, the idea of
injecting a carrier or not is
related to the issue of
whether or not we want to do
synchronous or asynchronous
demodulation.
The asynchronous demodulation
corresponding to the simple
use of an envelope detector.
And to remind you of the wave
forms that are involved,
again, I show two that
we saw previously.
And for the case, this is for
one value of the amount of
carrier that's injected.
And this is for an amount of
carrier injected that's less.
And this, in fact, corresponds
to what we refer to as 50%
modulation, and this is the
case of 100% modulation.
Well, the modulating system
that we're using in this
demonstration is basically
of the form that
we're indicating here.
And a simple block diagram for
it is more or less identical
to what we just saw.
Specifically, the modulating
signal is
multiplied by the carrier.
And there also is the capability
of injecting some
additional carrier, meaning
adding it to the output of
this product.
And so the modulated output can
have a variable percent
modulation--
the percent modulation being
changed, depending on how we
set this variable gain.
Now, in addition to sinusoidal
modulation--
in fact, for the particular
system that we're using, we
have somewhat more
flexibility.
We can use, in addition to a
sinusoidal carrier at this
point, we can alternatively
choose a square wave carrier
or a triangular carrier.
And, as we'll indicate in a
moment when we illustrate
this, there are some specific
advantages to using, for
example, a square
wave carrier.
So this is a somewhat simplified
version of--
or rather block diagram of the
modulating system that we're
demonstrating.
The external modulating input
here, a choice of carrier with
also the capability for
injecting some additional
carrier into the output.
OK, now let's go back
to the equipment and
take a look at this.
Well, Sandy, maybe to begin,
you can just point out what
some of the controls are
on the modulator box.
SANDY HILL: OK, there
are some interesting
points to look at here.
This is an input for
an external signal.
We'll be taking a signal right
out of the signal generator
and putting it in here.
And that will be the signal
that will be modulated,
according to the carrier.
The carrier is generated
internally in this device.
And there are several ways
of controlling it.
One is the amount of
carrier injection.
One is the wave form of the
carrier itself-- and this is
typically sinusoidal in the
broadcast industry, but others
are interesting to
look at as well.
The output that will be
displaying on both the
spectrum analyzer and scope
comes out here.
And then farther over to the
left, there are some knobs for
changing the frequency of
the carrier signal.
PROFESSOR: OK, let me also
just point out again for
emphasis that changing the
carrier level, as we've talked
about, is mathematically
equivalent to changing the DC
level of the modulating
signal.
And that's also what affects the
percent modulation as we
had just discussed.
Now what we have set up is a
sinusoidal modulating signal
and a sinusoidal
little carrier.
And, as usual, we have the time
wave form displayed here.
And so this is the
modulated signal.
And then on the spectrum
analyzer, we have
the spectral display.
And this is the carrier
signal.
That's the carrier frequency.
And these side bands then
correspond to the side bands
associated with the
modulating signal.
So this is the spectrum of the
total modulated output, right?
SANDY HILL: Right.
It's interesting to vary some
of these parameters.
You can see the sinusoidal
modulating
shape at this point.
Let me switch that to
a triangular shape.
And, again, it's a little hard
to sink in both the modulating
signal and the carrier, so you
see the carrier kind of
wondering by, but there it is.
Another thing that can be varied
is the amplitude of the
modulating signal.
I'll make it smaller--
you'll see the side
bands go away--
until finally we have a pure
sinusoidal carrier--
as I bring them back in.
Again, this is triangular.
There would be harmonics there
that maybe they're a little
hard to see in the spectrum
analyzer.
I'll go back first to a square
wave modulating signal, which
is, again, you can see the
square wave on top and one on
the bottom.
PROFESSOR: And so all of this,
then, represents side bands.
Is that--
SANDY HILL: That's right.
Those are the side bands due to
the square wave modulation.
Going back to the simplest,
the sinusoidal carrier.
Another thing we can do is to
vary the frequency of the
sinusoidal signal that's
modulating it.
I'll make it higher.
And you'll notice that the side
bands wander away from
the carrier signal
in the spectrum.
The spectrum, the carrier signal
of that, doesn't have a
frequency that's changing
as I do this.
It's just the width of
the band, due to
the modulating signal.
PROFESSOR: So this
is the carrier.
And these are the side bands.
SANDY HILL: That's right.
Now as we go out very far, those
side bands get gobbled
up by the carrier itself.
I'll come back to a nice
reasonable point there.
PROFESSOR: OK, now, we can
change also the carrier
frequency and, as Sandy's
indicated, various parameters.
Now let me just point out, since
I didn't previously,
that the frequency scale that
we're looking at here is a
frequency scale out
to 20 kilohertz.
And we had talked about--
or Sandy had indicated--
that we can change the
carrier signal shape.
And let me change the carrier
signal from a sine wave to a
square wave.
Now you haven't seen any change
on this particular
display , but let me change
the frequency scale.
And what you see now is the
modulating signal showing up
around harmonics associated
with the carrier.
And those harmonics will go
away when we go back to a
sinusoidal carrier.
SANDY HILL: This is actually
called a ring modulator.
It's very simple to multiply
a signal by a square wave.
It's just a chopping process.
And so a square wave carrier
signal is very
convenient to generate.
And then you simply filter out
the higher order harmonics.
PROFESSOR: Right, I'll
go back to the
scale that we had before.
And Sandy had also commented
that we can
change the carrier level.
And let's do that on
the modulator box.
We could do that either by
changing a DC offset on the
modulating signal or by changing
the amount of carrier
that's injected.
And as we decrease the amount
of carrier, in fact, going
down to no carrier at all
or almost no carrier.
That's suppressed carrier.
We have only the two side bands
and the signal is now
highly over-modulated.
We bring the carrier back up and
when we do that, then we
are reducing the percent
modulation and simultaneously
obviously related to that is
changing the carrier level.
Now I had indicated in previous
lectures that
reducing the carrier is
efficient in terms of power
transmission, but requires a
synchronous demodulator,
whereas if there's carrier
injected, as we have here, so
that we're not over-modulating--
the percent modulation
is less than 100--
then because of the shape of the
time wave form, as you can
see here, you can do the
demodulation with a more or
less simple envelope detector.
And in fact, a envelope detector
of the type that
we've talked about before is
exactly what is used in AM
radios, because of the fact
that it's so inexpensive.
And so here the power
transmitted required is
higher, but the demodulator,
based on using an envelope
detector, is considerably
simpler.
Well, speaking of AM radios,
what we'd like to now
demonstrate is modulation and
demodulation with an AM radio,
which Sandy happens
to have here.
And let's see, I guess, what
you're going to do, Sandy, is
take it apart for us, right?
SANDY HILL: Right.
I've taken off the back.
And I'm just now going to slip
out the guts of it all, and
try and set it up so you can see
it conveniently, such as
right there.
PROFESSOR: Now, this is your
daughter's radio that you
promised to give back.?
SANDY HILL: I would say was
my daughter's radio.
And now let's start attaching
clip leads, because what we're
going to want to do is to be
able to see the signals coming
out of the radio.
We want to see both the audio
and then the modulated signal
and try and see them on
the oscilloscope.
So I'll start setting
that up now.
PROFESSOR: OK.
Let me--
while you're doing that-- also
just comment that the kind of
AM radio that we're looking
at here is called a
superheterodyne receiver.
And the way that it does the
demodulation is not exactly
the way we've talked about
it in the lectures.
It's very close.
The idea is this the RF signal,
the radio frequency
signal, first gets modulated
down to what's called an IF
stage-- the intermediate
frequency stage.
And then it's that signal that
goes to an envelope detector
of the type we've talked
about to generate
the demodulated signal.
So, I guess what Sandy has
some probes on are the RF
input and a ground--
SANDY HILL: That's right.
The red lead here is a ground.
It's common for both the signals
we'll be looking at.
This is at the audio.
We're actually looking at the
signal going directly into the
speaker across these
two leads.
And then this probe down here,
which I found by hunting and
pecking, is the IF signal, the
intermediate frequency signal,
with a station on it that I'll
now try and get something that
sounds reasonable.
[RADIO FEEDBACK]
SANDY HILL: OK.
A little sports.
PROFESSOR: Never quite know what
you're going to get when
you turn this on.
SANDY HILL: That's
right, you don't.
Make some adjustments there.
And what you can see right
here is the audio signal.
I'll give it a little
bit more game.
And this is the actual
intermediate frequency,
modulated by the audio.
And there's a correspondence
between them that goes by
awfully fast, but I think it's
pretty simple to see.
PROFESSOR: So basically the top
trace is the envelope of
the bottom right.
SANDY HILL: That's right.
This is what comes out of
the envelope detector.
And this is the signal into the
envelope detector, in this
particular radio.
What I'd like to do for a last
experiment is what we've been
doing at this point--
I'll turn this off
for a moment--
is we're taking something that's
coming in over the
airwaves, as they used to say,
and we're simply viewing it.
What I'd like to do now is
generate our own radio
frequency signal, tune it
up so this radio is
going to hear it--
whatever that means--
and display it here.
What we're going to do then is
use the audio oscillator,
along with the amplitude
modulator.
And we're going to take from the
output now the lead here.
And this will act
as the antenna.
This device was not designed
to put out a lot of power.
But fortunately we don't have a
lot of distance to go over.
What I'm going to do is turn
myself into an antenna--
I'm basically 150 pounds
of salt water--
and when I touch this, the
signal coming in here, which
is radiating a little from the
wire, is going to suddenly
radiate from my whole body and
hopefully will be enough
to be picked up.
So what I'll do is I'm going
to turn this on--
excuse the noise.
Now I've set this up so it's
tuned to a particular radio
station, and I hope
I can find it now.
It takes a little fussing.
That's not it.
That sounds like it now.
OK.
PROFESSOR: So this gets billed
as Sandy Hill, human antenna.
SANDY HILL: That's right.
What you're looking at here is
I've got the antenna at this
point, and what we're going
to do is you're
seeing the audio signal.
This is coming from the signal
generator up here.
And this is the intermediate
frequency signal again.
You can hear it's much stronger
when my body becomes
the antenna.
And I'll leave it
on for a second.
And I can switch to
square wave--
doesn't look much like
a square wave.
Various things.
There's significant distortion,
because of all the
transformations that the signal
is going through.
But it does indeed work, and
we're picking up a frequency
that the radio is tuned to.
And that's it.
PROFESSOR: So Sandy has
now been modulated and
demodulated.
SANDY HILL: That's right.
PROFESSOR: Well, hopefully, all
the things that we've gone
through in the process of this
tape and this set of
demonstrations gives you a feel
for at least some of the
things that we've talked about
so far in the course.
And Sandy, I'd really like to
thank you for joining us, for
sharing your insights with us,
as well as sharing your
equipment with us.
Thanks a lot.
SANDY HILL: It was a treat.
Thank you.
