Let's take a look at a MATLAB Simulink illustration of the 10 band graphic

equalizer now. Now, I'm not going to drag you into any

of the details of the MATLAB, but I wrote a simple MATLAB file.

The first thing that happens is it constructs the coefficients for the

filters. Now, there's one thing I have to tell you

here, is that this actually, the im, implementation that I'm showing you.

Is, is a digital implementation of the same, equivalent Butterworth Octave

Filters. And, there's, a whole course of signal

processing that one has to go through to be able to construct these filters in the

digital domain. But, the, the point is that they have

identical performance to the Octave Bandpass Filters that we were just

discovering, and so it doesn't matter. That the implementation is digital,

frequency response, and the way things sound obviously are exactly the same.

So, what this this MATLAB file does first, is it goes through and it

constructs the 10 filters for us. And so, what I've plotted here is the

magnitude response of the filter versus frequency.

Now, where the frequency is normalized to 22,050 Hertz.

Now we're I said we're not going to go into the details of digital sound.

But that is exactly one half of the sampling rate of an audio CD.

An audio CD is 44,100 Hertz, typically. And, half of that is the maximum

frequency that is captured by that CD. And so, we're going to normalize our

frequency to that. So a frequency of 22,050, then,

corresponds to one. One half is 11,000 Hertz, 11 kHz.

Now, the first band in the 10 band graphic eq, equalizer is down here at

about 31 and a half Hertz. And so here is the signal or the

frequency response plotted on a linear frequency access and here it is on a

logarithmic axis. So this has the same appearance as the

filters that we were drawing a few minutes ago.

And so now the program goes through and it constructs all of the successive

filters. So there's the next filter at two times

this frequency. The next, so this is, 31 and a half,

63,125. There's 250, 500, 1000, 2000, 4000, 8000,

and there's 16,000. And notice I had to construct these

filters so they actually dropped off, before I got to 22,000 Hertz.

So there's a little bit of funny stuff going on in these higher filters.

But here is the set of filters that we set up for the graphic equalizer.

So you can see them all. Their peaks each one is at twice the

frequency of the previous one and on the log access they all line up nicely, they

all look similar. And so when I add them all together here

is a node linear frequency, access response looks like this.

And on the log response and I plotted log of the magnitude so, the, these are,

these scales are both linear. This is linear in frequency, linear in

magnitude. This is logarithmic in magnitude, and

logarithmic in frequency. And so this looks quite flat in the log

magnitude response. So, this is the setup for the 10 band

graphic equalizer. So now, those filters are all set.

And here's something that I, I realize this is a little hard to see.

let me make it as big as we can. I can, try to zoom in on things.

But what this is, is Simulink is part of MATLAB Programming environment.

And it's a graphical interface that lets you just construct signal processing

algorithms just by dragging and dropping blocks.