0:01

Now that we've completed our discussion of the spectra and the frequency content

of signals, I want to go back now and talk about how we can apply filters using

the electrical circuits to alter the tone of a signal.

So, to illustrate this, we're going to start with a very simple starting signal,

and this is going to have some fundamental frequency, and then equal

power at all harmonics of that fundamental.

So, this just helps to illustrate how the filter functions.

So, let's say we start with a signal this sort And we're going to apply, say a low

pass filter. A low pass filter has a characteristic

that looks like this. It's going to basically multiply every

frequency component by an amplitude equal to the pipe of the filter at that

frequency. And so the resulting filtered signal is

going to look like this. We're going to have less power in the

higher harmonics, and the lower harmonics will be less affected by the filter.

So, what I want to do now is first generate this.

harmonic rich overtone spectrum with equal power, just so you can hear what

that sounds like, and then we'll apply low pass and high pass filters with

different cutoff frequencies to that signal and explore what that sounds like

too. So in this last simulation, we're going

to just add together all harmonics of the fundamentals.

So we start with the fundamental of 220 Hz, and then we add in 440, 660, 880, so

on and so forth. And all harmonics have the same amplitude

of one. So here's that simulation.

[SOUND]

In this MATLAB demonstration we show the effect of the simple low pass and high

pass filters. That we derived previously.

Now, we show this by applying these filters to the harmonic rich starting

sound that we generated just earlier today.

So, the what you're going to see is the The the frequency spectrum of the

starting tone, and so this is all harmonics equal amplitude.

So, it starts at 220 and goes up to almost ten kiloherz, and then, to this

starting signal, we apply a simple low-pass filter.

And the one that we assume that we're using is a RC low pass filter which

actually if we had a RL filter and choose the values of R and L appropriately we

could get exactly the same result for Configured as a low pass filter.

4:17

And in this case though, we have the RC filter with a time constant of 1

millisecond, and this corresponds to a cutoff frequency, this is the 0.707, 1

over square root of 2, frequency of 159 hertz.

And here is the resulting final spectrum. And so now, we'll play the starting sound

and then we'll play the filtered sound. [SOUND] So you can tell the tone

difference. and that's just due to the fact that the

higher harmonics involved have all been suppressed.

Now, we can go and, we can change The this had a cut off frequency of a 159

hertz. I could change that to be say ten times

that and so I made the r c type constant ten times smaller and so the cut off

frequency is ten times smaller and so instead of a 159 It's around 1,590 hertz,

and this is the resulting spectrum of the filtered sound, and this is what they

sound like. [SOUND] So, there's not as much

difference because there's still repressible power in the higher

harmonics. Now just to go a little further, let me

make this say 0.003, and so I'll move the cutoff frequency out even more, and in

this case, the cutoff frequency is 53 kilohertz.

I went too far, and it essentially does nothing out to 10 kilohertz, so you'll

hear that these should sound the same. [NOISE] And I think I had one too many

zeroes here. So I was going for this.

6:44

So the time constant is .03 seconds and the cutoff frequency is only five hertz.

So I've attenuated virtually everything. And I just have even a small amount of

the fundamental gets through. And if we listen to that.

[SOUND] You have mostly fundamental. Now the loudness, although the these the

unfiltered signal has much higher amplitude than the filtered signal.

The way I've set up mat lab to play the sounds is it normalizes it so it plays

the sounds with equal loudness, so, so don't be deceived by that.

We're just listening for the tone quality anyway, we're not listening for the total

loudness of sound. Okay, now we'll do the same thing but

using the high-pass filter. So this is our, could be constructed the

same way as the low-pass RC filter, but you just switch the position of the R and

the C. so here it is with a time constant of ten

to the minus four. So the cut-off frequency's around 1591

hertz and so out here around two kilohertz we're at the 0.707 value.

8:13

And, let's listen to that. [NOISE] So we hear the second one, it's a

much higher there's a more high frequency content that makes a much buzzier kind of

sound. Let me move this out a little further

yet. So now the cut off frequency is around

five kilohertz. [SOUND] And let's go the other way.