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.