Equalization Part 1: Introduction To Equalization

The equalizer is perhaps one of the most important, if not THE most important, tool in the audio business.  It doesn't matter at what stage of the production you are in, equalization will always be a part of it.  If you get this part wrong, the other effects might be as perfect as they can be, the mix will not sound good.  When I listen to other people asking for help, I see that a lot of them don't seem to understand even some basic principles, hence the reason for this guide. In the following pages, I'll try to explain how equalization works, what it does to the signal, and finally what to achieve with it. Sometimes I'll get a bit technical, and some people might not understand what I say, but it's important you grasp the concepts (and the terms too) to be successful at equalization. EQ is a tool you should master without actually thinking about it. I'll use graphics and sound samples to make it easier to understand. Fasten your seatbelts, and enjoy the ride!

We want to know about the Equalizer!

So here we go. When we talk about an equalizer, we are in fact talking about filters: devices that filter the signal.  There are two kinds of filters: passive and active.  Passive filters can only cut, active filters can boost also.  In reality, EQ's are active.  But over time, EQ'ing has become a standard term so that passive filters are part of the process too. In the following explanations, there will be sound samples available to make things more clear. Most of the sample is untreated so you can get acquainted with the sound. When the man starts saying "the Dj booth is conducting...", the filter is active.

Passive filters

• The first filter is called a lowcut, or highpass, filter.  A little bit of common sense and you'll know what it does.  It cuts above a certain frequency, called the cutoff frequency.  The rest will remain unaffected. To make it difficult, theoretically this is the frequency where there is already 3dB of cut. This frequency can be fixed, or variable. Another thing you need to know is how "hard" the filter cuts.  This is defined by the slope of the filter.  We talk about the order or pole of a filter.  In the beginning such filters were made with a combination of resistors and capacities.  One resistor and one capacity formed one order.  A first order filter has a slope of 6 dB per octave.  Let's take an example, we take a lowcut filter with cutoff frequency at 1000 Hz.  It means that 1000 Hz will already be attenuated by 3 dB.  For every extra octave we go under the cutoff, we lose another 6 dB.  So compared to the unaffected signal, 500 Hz will have 9 dB of cut, 250 Hz will have 15 dB and so on.  Now the order of the filter is just a multiple of the 6dB/oct figure.  A 2nd order filter will have a 12 dB/oct cut, a 3d order a 18 dB/oct.  The classic Moog filter is a 4th order filter (the sound samples will clarify all of this).  Usually lowcut filters are used to remove contact rumble of microphones, but they also serve a very important role in mixing. Many mixers have lowcut filter with a fixed cutoff around 75-80 Hz.  Make it a habit to activate it on all instruments that contain high frequencies (hihats, cymbals).  Try to switch them on other instruments too where low bass response is not the main focus (vocals, guitars, lead synths,...). Doing that will clear up the mix and leave more room for the bass instruments.
   
  
  
  Lowcut response, notice that the cutoff point is already 3dB down

  Lowcut with cutoff at 1kHz, 1st order (6dB/oct) (click to listen)

  Lowcut with cutoff at 1 kHz, 6th order (36dB/oct) (click to listen)

• The second filter is the the opposite, the lowpass or highcut filter. This time they cut above the cutoff frequency. Lowpass filters are commonly used in synthesizers (if you forget the resonance control), and as anti-aliasing filters in A/D converters.
   
  
  
  Highcut response

  Hicut, cutoff at 1kHz, 6db/oct (click to listen)

  Hicut, cutoff at 1 kHz, 36 db/oct (click to listen)

  The two following filters are a sort of combination of the first two. The graphical response can be deducted by making a combination of both pics above.  

• Bandstop or rejection filters.  Like the name implies, they cut a certain frequency range. Here we have two cutoff frequencies and we need to add another parameter: bandwidth. That's nothing else than the difference between f2 and f1, in other words, the range itself.  We generally also use the term center frequency (it's the middle of the range).  If you want the exact figure, it's SQRT(f2xf1).  A bandstop filter with a very narrow bandwidth is a notch filter.  Usually you'll use such filters to remove annoying frequencies like hum, without affecting too much of the rest of the signal
  
  

  Bandstop filter with center frequency at 1kHz, bandwidth 5 octaves (click to listen) 
  

• The opposite of the bandstop filter is the bandpass.  Again, we got two cutoff frequencies: a bandwidth and a center frequency.  We could also define a Q factor (resonance), which is the ratio (Fcenter/bandwidth).  The Q factor can also be applied to the bandstop.  A high Q means a narrow action, a low Q means a broad action.  Such filters are used to limit the frequency range for broadcast, or for effects like the telephone voice.  When you look at the graphic you see that it's pretty angular.  The whole thing can be rounded too, but then we usually talk about a Bell filter.
  
  Bandpass filter with center frequency at 1 kHz, bandwidth one octave (click to listen)
   
• Last type of passive filters are shelved filters.  You have low shelved and high shelved filters.  The name implies what frequency ranges they work on (below or above the cutoff frequency).  The difference with the high and lowcut filters is they only cut to a certain amount, then return to unity gain again (meaning they remain flat again).  Let's take our example again.  We use a high shelf filter with the cutoff frequency at 1000 Hz.  A very important thing to remember with shelved filters is that the cutoff frequency is not 3 dB cut from the normal position, but the point that is 3dB away from the maximum action.  Here we have to specify an amount of cut; let's say 10 dB.  Our cutoff frequency of 1000 Hz will be at -7 dB, if you follow the rule we just stated.  Again, with a certain slope (fixed by the manufacturer), we move to -10 dB.  Once this point is reached, it goes back to a flat figure.  So every frequency we look at, further from that point, will still be at -10 dB.  A normal cutfilter will remain cutting with that certain slope.  These graphics will explain better:
  
  

  Lowshelf, notice the cutoff frequency is 3dB off the maximum action
  High Shelf, same remark as with the Lowshelf

  Lowshelf at 1kHz, 10 dB cut (click to listen)

  High Shelf at 1 kHz, 10 dB cut (click to listen)

Active Filters

We'll start from where we ended in the previous part. We'll only be showing graphs of the parametric, because the others can be deduced from other filters.

• Shelved filters exist in active form too, but now we'll call them shelved EQ's.  To keep it simple, active just implies there is a gain stage added in the circuit, so you can not only cut, but also boost.  Again, if you look at the name, you'll know what they'll do.  The Hi shelf EQ cuts/boosts above the cutoff frequency, the low shelf below.  This is the type of EQ you usually find on Dj mixers or simple production mixers as the Hi and Lo EQ's. T he cutoff frequency and slope has been fixed by the manufacturer.  It's also the type of filter used as tone controls for your hifi equipment (slightly different curve though, Baxandall).
  
• The second EQ is the Bell EQ, also called peak/dip EQ.  If you payed attention up to now, you'll know what to expect.  Yup, it's basically an EQ that can go from bandstop to bandpass behavior (with the rounded edges though).  It's usually the kind of EQ you'll find as the mid EQ on Dj mixers and cheap production mixers.  Now we start to get in the more expensive EQ's.
  
• The semi parametric or sweepable EQ is an EQ where you can choose the cut/boost gain, and the center frequency.  This allows for more control already.  There are two systems though: Constant Q, variable bandwidth, Constant bandwidth, and variable Q.  They are fixed by the manufacturer.
  
• And now, the Rolls Royce of the EQ's: the full parametric EQ.  You cannot only choose the gain and the center frequency, but also the Q.  In other words you can also decide on how large a range you'll work.  On some occasions, you'll only be able to select the Q in steps (like Hi and Lo), then we prefer talking about quasi parametrics.  This EQ offers the most control, but is also the most expensive to build.  Keep in mind that a low Q covers a wider bandwidth.  Higher bandwidth means more energy.  A low Q sounds more musical though. You can get away easier with a high Q when cutting, rather than boosting.

• Center frequency at 1kHz, Low Q

  Center frequency at 1kHz, High Q

  Parametric at 1kHz, Low Q, boost (click to listen)

  Parametric at 1kHz, High Q, boost (click to listen)

  Sometimes it's easier when you can define the action range of the equalizer in octaves instead of the Q factor.  Here follows two comparison tables to know what Q corresponds to which bandwidth.  You might find some figures to be slightly different, that's because of the rounding applied. (click to listen)

  Bandwidth	Q
  0.02	72.13
  0.03	48.09
  0.04	36.07
  0.05	28.85
  0.06	24.04
  0.07	20.61
  0.08	18.03
  0.09	16.03
  0.10	14.42
  0.20	7.21
  0.30	4.80
  0.40	3.60
  0.50	2.87
  0.60	2.39
  0.70	2.04
  0.80	1.78
  0.90	1.58
  1.00	1.41
  1.20	1.17
  1.40	0.99
  1.60	0.86
  1.80	0.75
  2.00	0.67
  2.20	0.60
  2.40	0.54
  2.60	0.49
  2.80	0.44
  3.00	0.40

  
  

  Q	Bandwidth
  0.50	2.54
  0.55	2.35
  0.60	2.19
  0.65	2.04
  0.70	2.00
  0.75	1.80
  0.80	1.70
  0.85	1.60
  0.90	1.53
  0.95	1.46
  1.00	1.41
  1.10	1.27
  1.20	1.17
  1.30	1.08
  1.40	1.01
  1.50	0.94
  1.60	0.89
  1.70	0.84
  1.80	0.79
  1.90	0.75
  2.00	0.71
  3.00	0.48
  4.00	0.36
  5.00	0.29
  6.00	0.24
  8.00	0.18
  10.00	0.14
  20.00	0.07
  30.00	0.05

  There are other types of EQ still.  For the sake of completeness I'll state them here, but they are generally not used in the production process.
  

• The graphic EQ is an array of lots of sliders each representing a different peak/dip EQ.  The most complete ones have 31 bands per side (so stereo is 2x31).  Each band covers 1/3d of an octave.  They are called graphic EQ's because the position of the sliders roughly represent how the frequency spectrum looks after the correction (if you started with a flat signal).  Such EQ's are generally used to compensate for room acoustics, or to linearize a system that has some unwanted peaks or dips in the spectrum.  Obviously, those EQ's are very useful for a live PA.
  

• The paragraphic EQ is just a graphic EQ with full parametric EQ's instead of peak/dip ones.  Obviously this is VERY expensive to make, and frankly pretty useless.

There are certain types of filters that get a special name, but either define a method of construction or are a result or combination of the above filters.

A formant filter, for example, is a filter that works on the formants.  The formants are nothing more than the harmonic content of sounds.  Usually they act on the formants of the human voice. So those filters are useful to make synths do "oooh, aah, eeh,..." sounds.

Allpass filters have a weird name.  Basically it's a combination of notch filters.  They leave most of the signal untouched, but cut some fine holes in the spectrum due to the notches.  It's with such filters that the phaser effect is formed (they modulate the center frequencies of the notches).

A comb filter is an extreme kind of allpass filter.  The special thing about this one is that this one happens in nature too.  Basically, if you take two identical signals, and you apply a very small delay to one of the two, and mix them back together, a comb filtering will occur, and at certain frequencies, phase cancellation will occur.  You say: than you can make it with an allpass filter? Yes and no.  The main difference is that the notches in the all pass filter are spread out evenly through the frequencies spectrum.  In the comb filter, they will have a harmonic relation.  The center frequencies of the higher notches, are all on harmonics of the first notch, and there are a lot.  If you think this effect doesn't happen much, think again.  For example, when you listen to your speakers in a room, it always happens.  You hear the sound coming directly from the speakers, but you hear the reflected sound too, with a certain delay.  This in effect creates a comb filter.  But we're so used to it that we don't hear that anymore.  If we want to use comb filtering as an effect, we'll need to exaggerate it.

A lot of times you'll hear people saying to roll off some frequencies. Usually that means using a high or low cut filter (or a shelved one).  If for example they say, gently roll of the frequencies below 100 Hz, it means you insert a lowcut with a gentle slope, with a cutoff frequency around 100 Hz.

Final Thoughts:

While the equalizer is an in-valuable tool, it is certainly not a "cure-all" tool for producing. Other effects such as compression, reverb, and flanger are often needed to mold a sound to match your imaginiation.

Knowing what an Equalizer is and knowing how to use one are skills quite different from each other. Part 2 of "In Depth: EQ" will go further into using equalizers to achieve a proffesional mix.

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