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A graphic equalizer is built out of what are called octave filters with constant
Q. At least that's one way you can build a
graphic equalizer is with, with octave filters.
Actually, if you look at your you go on iTunes, for example, and you pull up the
graphic equalizer window, that uses octave filters.
And, I'll explain what that is right now. Now, an octave filter filter bank, is one
where each filter and each successive filter in the bank increases by a factor
of 2. So, let me just give you a simple
example. Here is a filter at 200, I'm sorry, about
500 hertz. Here is one with a center frequency of 1
kilohertz. So, 500 hertz to one kilohertz.
There is a factor of 2. Then, the next filter would be 1 to 2
kilohertz. And then, from 2 kilohertz to 4
kilohertz. So, these are octave related filters.
Each one has double the resonant frequency of the previous one.
And the other thing is that I've drawn these filters so they all have the same
Q. 1 over square root of 2.
Now, what you see is that the absolute width of the filter gets wider as the
center frequency moves up. But since they're fixed Q, the, the ratio
of the width of the filter divided by its center frequency is fixed.
And that ratio, delta f over f, is 1 over Q.
So, 1 over 0.7 is 1.4. And so, delta f is always 1.4 times the
center frequency. Now, the delta f is measured where the
filter response drops to a factor of 2 n power square root of 2 n amplitude, so
it's like the 0.707. So, it's looking at the red one it's from
a point. So, here's it's around 0.7 on this axis.
And so, it's the width measured at this point here, and I'll show that in a, in
a, in a minute here in a little more detail.
But anyway, this is an illustration of a set of octave filters with constant Q.
Now, let's take a look at another set that I'm going to make up.
Now, I want to plot these on a logarithmic frequency axis.
That's going to make things a little bit simpler to see.
Now, also, the other reason for that is your hearing response, your pitch
response and hearing is logarithmic. So I drew this a set of, of band pass
filters. Now, this set, the first one is at 250
Hertz. This one is at 500 Hertz.
So, this access here is kilohertz, and so here's half a kilohertz, this is 500
Hertz. And then, here is about 1 kilohertz and
around 2 kilohertz. Now, that lines up with a piano keyboard.
If the way that notes are denoted on a piano, middle C on a piano is called C4.
It's the fourth one up from the lowest keys on the piano.
So, C4 has a frequency of about 261.6 hertz.
And so, I've drawn a band pass filter with that center frequency.
So, this is the first. Then, the next octave up, C5, that's a
center frequency of 532. And then, the next one up, center
frequency of about 1046, and then 2092. Now, the thing is, when you draw these
filters on a logarithmic frequency axis, then they all look the same.
The green filter and the blue filter, the purple one here, I could slide the green
one, and it would lie right on top of the purple one.
And so the, the constant cue requirement on these filters makes them all line up
perfectly if I slide them back and forth on this frequency axis.
And the last thing I wanted to say is, now, looking at one of these filters, and
I look at the 0.707 point, one that's 1 over square root 2 and measure the width
of the filter at that amplitude. So, here's the delta f.
If I take delta f over the center frequency, that width is 1 over Q.
And each of these filters is going to have on a logarithmic scale, is going to
have the same dimension along the frequency axis.
But delta f over f is fixed. Okay.
So, there's an octave filter. Now what we want to do now is I wrote a
MATLAB Simulink demonstration that shows how these an octave filter band, a
ten-band octave filter band sounds. And so, this is kind of nice.
You can see in real time, how the modification to each filter changes the
way things sound. So, let's take a minute now, and listen
to that simulation.
Robert ClarkProvost and Senior Vice President for Research and Professor
Mark BockoDistinguished Professor and Chair
