EQ and Math
- Thread starter jhrv
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LSD-Studio
HCAF crusher
- Mar 27, 2007
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evolutions_end
now with extra avatar!
Razorjack
Bass Behemoth
Is there a bigger question? The answer is, of course, yes. Are you looking for a more detailed explaination?
Something like this, Maths of the Discreet Fourier Transform with audio applications is what you want if you want to look into Digital audio. This link, whilst detailed, just scratches the surface of digital audio theory.
Something like this, Maths of the Discreet Fourier Transform with audio applications is what you want if you want to look into Digital audio. This link, whilst detailed, just scratches the surface of digital audio theory.
Machinated
Member
Chryst Krispies
Vanilla Gorilla
Seizure.
Member
This is the kind of point were i stop and started thinking about making music again instead of the theory's behind it to make it sound good haha
Everything *of significance* can be traced to math.
EQ is just making certain ranges of audio quieter. Understand logs, and read through a simple EQ VST to work out how things are done, and you're cut.
Jeff
EQ is just making certain ranges of audio quieter. Understand logs, and read through a simple EQ VST to work out how things are done, and you're cut.
Jeff
Okay...
...
FUCK!
You already pointed that out! It isn't even relevant! Every fucking goddamned time someone brings up 'math' - and yes, I just said math! - someone has to say 'maths' AND THIS CONTRIBUTES NOTHING AT ALL! It's not even like someone's using the wrong their/they're/there or is saying 'could of' instead of 'could have'... maybe the first time someone said 'math' instead of 'maths' it would have been somehow relevant BUT EVERYONE IN ONE OF THE ONLY TWO ENGLISH SPEAKING COUNTRIES THAT COUNT (Fuck you, Canada! I'm caffeinated as balls!) says MATH! It simply is not relevant! There are very important things to discuss here AND THE LETTER S IS NOT (Fuck you, too, Sesame Street!) ONE OF THEM! And if one of you so much as thinks about replacing 'math' in my post with 'maths' or offering some other such suggestion, I will make your fucking head explode with several books on analytic number theory. If you're lucky. Just pray that I'm not in the mood for differential topology, grammar whores. I am fucking wired and you will not be amused. Do you tell a physicist that centrifugal force doesn't exist? No, because he will strap you to a rotating reference frame and make you wish it fucking didn't. Do you tell a linguist that a preposition is a horrible thing to end a sentence with? No, because talking to them fucking sucks. So, paying no mind to being polite or humble, there is quite clearly a similar reason not to correct people who say 'math' - I will fucking math you to death. Let's move on.
First, just to make sure everyone ('maths'-crackpots and others alike) is on the same page, here's how JBroll thinks of voltage. The fancy-pants definition basically says that a voltage is a potential difference between two sources - so on one side of the voltage a charged particle (electron, proton, positron, credit card after she-who-guards-the-snatch gets her way) there is something that can be gained from going to the other side (like when we deal with the motion of charged particles through fields with potential and the potential becomes kinetic energy), but it's not as quite intuitive as lemmings jumping off a cliff. How are lemmings jumping off a cliff intuitive? I might just tell you. I'm still wired as fuck. That last paragraph took twenty seconds. I'm not going anywhere.
Here's what happens when a lemming jumps off a cliff: the lemming has a sudden attack of the dumbass and decides that it would be fun to walk around on the invisible ground in front of him. Yes, I'm being sexist and assuming that the lemming jumping off the cliff is a male, so deal with it. He goes to the invisible ground, finds that it is also immaterial ground, and begins falling. Eventually he hits the ground and, for the vast majority of possible cliffs, makes a splat at the bottom of size roughly indicative of the height of the cliff. The height of the cliff is the voltage - your lemming can gain (temporarily) kinetic energy by jumping off the cliff. Note here that generally the higher the cliff the bigger the splat.
Now, say we have a whole hell of a lot of lemmings jumping off the cliff. What do we have? A current. Formally, a current is the move of electric charge. We have our lemmings (electrons) moving through a region where their potential energy (height, multiplied by a constant for gravity) becomes potential energy (related to the time spent falling and the same constant for gravity), and then they go splat on the ground.
If there is something blocking the lemmings, like a concerned larger creature of some kind or a fence put up by such a concerned larger creature, there will be fewer lemmings making smooshy messes on the ground below. This is resistance - a suitable name. So if fewer lemmings jump down the cliff there's going to be less splat on the ground.
The formula relating voltage (V, SI unit Volts), current (I, SI unit ampere), and resistance (R, SI unit ohms) is V=IR. Therefore, increasing the height of the cliff and not putting up a fence of some kind or reducing the blockage without changing the cliff's height makes a bigger splat, and vice versa.
To restate the original definition of voltage, when there is a potential difference between two regions we say that the voltage is the amount of this potential difference. Simpler with lemmings jumping off a cliff, no?
Then, you need to understand how the audio gets turned into a digital signal. Long story short, what you're going to see is very often just a logic circuit that figures out some way of accepting an input voltage and then finding some way of roughly representing it compared to a reference voltage so that it can express things as a fraction of said reference voltage. If you have something going in with a higher voltage than the reference voltage, you have clipping. We avoid clipping. Let's pretend it doesn't exist.
Now, we have to keep in mind that audio signals are AC current. The lemming example above is, for stationary cliffs, an explanation of DC voltage. AC voltage is like that, but not - it alternates between a high point and a low point. We don't need to take the lemmings any farther, unless you'd like them to have bungee cords attached to a large pole or something - that analogy has served its purpose, though, so I'll stop with that nonsense. So when you have alternating current, it alternates at some frequency (or combination thereof - but shut up and work with me and we'll pretend that we can have just one), and that frequency corresponds directly to sound of some kind. This frequency is measured in Hertz (or some multiple thereof), which is just 1/s - this is just the number of cycles/beats/whatever per second. Sound, however, doesn't happen as just a single wave of this form - it's pretty much going to have to be a combination of them - so what we have is a superposition (or sum, or combination) of several different waves. So our chip is trying to figure out what potential difference a practically infinite sum of waves has at any given point in time, and by doing this thousands of times per second it gets enough data to interpolate a rough guess of what it was that it just recorded. Interpolation (the process of generating a function from a collection of points) is a whole different ball of wax, so look that one up elsewhere. Long story short, our DAW pulls everything between the collected points out of its ass and decides that some (possibly somewhat different, but usually really fucking close) other collection of waves is our signal.
Now, there are a lot of ways of actually doing equalization digitally, so for convenience I'm going to look at high-pass and low-pass individually and extrapolate from them ways of doing everything else. I'm going to steal an image from Wikipedia to show the basic electronic high-pass and low-pass filters.
Here's a low-pass - it sucks things out above a frequency related to the inverse of the product of the resistance and capacitance chosen (depending on whether you use Hz or radians/sec it'll be either 1/2piRC or 1/RC), and
is a high-pass filter, sucking out everything below a given frequency (again, 1/2piRC or 1/RC, depending on units)... the rate at which things drop changes between different implementations, but basically that's where things come from in the analog world. What we have to do with computers is discretize this... and I'm unfortunately not anywhere near wired enough to go into this one, so that'll be a post in the near future. Anyway, let's break and go on to the next thing.
What we can now generate from a low-pass and a high-pass is a hump. Not just any hump... the kind of hump we like to see on our graphic EQs. If we high-pass and low-pass at a given frequency we have a curve that is at its peak around that frequency and that decreases quickly as we go farther away. This means that we can boost individual frequencies with ease. Now, you ask, what about cutting frequencies? Simply take a hump and invert it, and you have a hump that goes in the other direction so you perceive a cut. The final frontier is then the shelf... or is it? Simply add a high-passed or low-passed chunk o' signal to what you already have, and you might like what you hear.
Thus, pending a possibly unnecessary discussion on discretizing functions, and a bit of work going into more technical details with more obvious mathematical reasoning, we have EQ.
DISCLAIMER: I'm not pissed at anyone... except you, you fucking lemmings, if you all go off and wind up extinct I'm going to be fucked, so don't even think of disappearing on me. Bastards. Again, I'm just wired as fuck...
Started writing this on Future Breed Machine. DEI isn't half over yet. Fuck me running. Oh, well, more later.
Jeff
...
FUCK!
You already pointed that out! It isn't even relevant! Every fucking goddamned time someone brings up 'math' - and yes, I just said math! - someone has to say 'maths' AND THIS CONTRIBUTES NOTHING AT ALL! It's not even like someone's using the wrong their/they're/there or is saying 'could of' instead of 'could have'... maybe the first time someone said 'math' instead of 'maths' it would have been somehow relevant BUT EVERYONE IN ONE OF THE ONLY TWO ENGLISH SPEAKING COUNTRIES THAT COUNT (Fuck you, Canada! I'm caffeinated as balls!) says MATH! It simply is not relevant! There are very important things to discuss here AND THE LETTER S IS NOT (Fuck you, too, Sesame Street!) ONE OF THEM! And if one of you so much as thinks about replacing 'math' in my post with 'maths' or offering some other such suggestion, I will make your fucking head explode with several books on analytic number theory. If you're lucky. Just pray that I'm not in the mood for differential topology, grammar whores. I am fucking wired and you will not be amused. Do you tell a physicist that centrifugal force doesn't exist? No, because he will strap you to a rotating reference frame and make you wish it fucking didn't. Do you tell a linguist that a preposition is a horrible thing to end a sentence with? No, because talking to them fucking sucks. So, paying no mind to being polite or humble, there is quite clearly a similar reason not to correct people who say 'math' - I will fucking math you to death. Let's move on.
First, just to make sure everyone ('maths'-crackpots and others alike) is on the same page, here's how JBroll thinks of voltage. The fancy-pants definition basically says that a voltage is a potential difference between two sources - so on one side of the voltage a charged particle (electron, proton, positron, credit card after she-who-guards-the-snatch gets her way) there is something that can be gained from going to the other side (like when we deal with the motion of charged particles through fields with potential and the potential becomes kinetic energy), but it's not as quite intuitive as lemmings jumping off a cliff. How are lemmings jumping off a cliff intuitive? I might just tell you. I'm still wired as fuck. That last paragraph took twenty seconds. I'm not going anywhere.
Here's what happens when a lemming jumps off a cliff: the lemming has a sudden attack of the dumbass and decides that it would be fun to walk around on the invisible ground in front of him. Yes, I'm being sexist and assuming that the lemming jumping off the cliff is a male, so deal with it. He goes to the invisible ground, finds that it is also immaterial ground, and begins falling. Eventually he hits the ground and, for the vast majority of possible cliffs, makes a splat at the bottom of size roughly indicative of the height of the cliff. The height of the cliff is the voltage - your lemming can gain (temporarily) kinetic energy by jumping off the cliff. Note here that generally the higher the cliff the bigger the splat.
Now, say we have a whole hell of a lot of lemmings jumping off the cliff. What do we have? A current. Formally, a current is the move of electric charge. We have our lemmings (electrons) moving through a region where their potential energy (height, multiplied by a constant for gravity) becomes potential energy (related to the time spent falling and the same constant for gravity), and then they go splat on the ground.
If there is something blocking the lemmings, like a concerned larger creature of some kind or a fence put up by such a concerned larger creature, there will be fewer lemmings making smooshy messes on the ground below. This is resistance - a suitable name. So if fewer lemmings jump down the cliff there's going to be less splat on the ground.
The formula relating voltage (V, SI unit Volts), current (I, SI unit ampere), and resistance (R, SI unit ohms) is V=IR. Therefore, increasing the height of the cliff and not putting up a fence of some kind or reducing the blockage without changing the cliff's height makes a bigger splat, and vice versa.
To restate the original definition of voltage, when there is a potential difference between two regions we say that the voltage is the amount of this potential difference. Simpler with lemmings jumping off a cliff, no?
Then, you need to understand how the audio gets turned into a digital signal. Long story short, what you're going to see is very often just a logic circuit that figures out some way of accepting an input voltage and then finding some way of roughly representing it compared to a reference voltage so that it can express things as a fraction of said reference voltage. If you have something going in with a higher voltage than the reference voltage, you have clipping. We avoid clipping. Let's pretend it doesn't exist.
Now, we have to keep in mind that audio signals are AC current. The lemming example above is, for stationary cliffs, an explanation of DC voltage. AC voltage is like that, but not - it alternates between a high point and a low point. We don't need to take the lemmings any farther, unless you'd like them to have bungee cords attached to a large pole or something - that analogy has served its purpose, though, so I'll stop with that nonsense. So when you have alternating current, it alternates at some frequency (or combination thereof - but shut up and work with me and we'll pretend that we can have just one), and that frequency corresponds directly to sound of some kind. This frequency is measured in Hertz (or some multiple thereof), which is just 1/s - this is just the number of cycles/beats/whatever per second. Sound, however, doesn't happen as just a single wave of this form - it's pretty much going to have to be a combination of them - so what we have is a superposition (or sum, or combination) of several different waves. So our chip is trying to figure out what potential difference a practically infinite sum of waves has at any given point in time, and by doing this thousands of times per second it gets enough data to interpolate a rough guess of what it was that it just recorded. Interpolation (the process of generating a function from a collection of points) is a whole different ball of wax, so look that one up elsewhere. Long story short, our DAW pulls everything between the collected points out of its ass and decides that some (possibly somewhat different, but usually really fucking close) other collection of waves is our signal.
Now, there are a lot of ways of actually doing equalization digitally, so for convenience I'm going to look at high-pass and low-pass individually and extrapolate from them ways of doing everything else. I'm going to steal an image from Wikipedia to show the basic electronic high-pass and low-pass filters.
Here's a low-pass - it sucks things out above a frequency related to the inverse of the product of the resistance and capacitance chosen (depending on whether you use Hz or radians/sec it'll be either 1/2piRC or 1/RC), and
is a high-pass filter, sucking out everything below a given frequency (again, 1/2piRC or 1/RC, depending on units)... the rate at which things drop changes between different implementations, but basically that's where things come from in the analog world. What we have to do with computers is discretize this... and I'm unfortunately not anywhere near wired enough to go into this one, so that'll be a post in the near future. Anyway, let's break and go on to the next thing.
What we can now generate from a low-pass and a high-pass is a hump. Not just any hump... the kind of hump we like to see on our graphic EQs. If we high-pass and low-pass at a given frequency we have a curve that is at its peak around that frequency and that decreases quickly as we go farther away. This means that we can boost individual frequencies with ease. Now, you ask, what about cutting frequencies? Simply take a hump and invert it, and you have a hump that goes in the other direction so you perceive a cut. The final frontier is then the shelf... or is it? Simply add a high-passed or low-passed chunk o' signal to what you already have, and you might like what you hear.
Thus, pending a possibly unnecessary discussion on discretizing functions, and a bit of work going into more technical details with more obvious mathematical reasoning, we have EQ.
DISCLAIMER: I'm not pissed at anyone... except you, you fucking lemmings, if you all go off and wind up extinct I'm going to be fucked, so don't even think of disappearing on me. Bastards. Again, I'm just wired as fuck...
Started writing this on Future Breed Machine. DEI isn't half over yet. Fuck me running. Oh, well, more later.
Jeff
Erik Monsonis
Member
