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Suppose you have a flat EQ, vs an EQ that is boosted by the same amount on each frequency (so that the new frequency is still a flat line, but just shifted upwards. Will these two settings sound the same, and are they the same mathematically/physically?

Edited slightly to make clear that there are two different questions

As another question, I'm also curious because a lot of "acoustic" EQ settings has every frequency boosted (it's no longer flat, but every frequency gets boosted by some amount). I'm wondering whether it is necessary/redundant to boost every frequency, or is only the relative settings important. For example, this is the Spotify acoustic EQ settings. I am wondering what is the effect of boosting all of the frequencies. Can you generate the same final sound by only boosting some of the frequencies? Why are all of them boosted to some degree? As an extension, can you generate the same sound by depressing all of the frequencies, in some combinations?

enter image description here

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    I’ll leave the answer to the folks who are more technically inclined in the audio department but you can see that this is close but not truly flat with everything boosted. It slopes down, up and down again from low to high. Also if there are any overlaps or gaps in the center eq frequencies because of their bandwidths that will create peaks and valleys in the curve. Commented Jun 9 at 18:38
  • Although I like Lazy's answer it may not be exactly what you are getting at, yes, if you boost all frequencies identically of a given signal then it is the same as just increasing the volume on that signal. A signal is made up of its time representation and its frequency representation. If you boost all the components of the frequency representation by the same amount then you have just amplified the signal. However it will not be easy to boost all frequencies equally with an analog or typical digital eq.
    – OwenM
    Commented Jun 10 at 0:13
  • Since frequency is based on time, and therefore a frequency can virtually be between near to 0 and infinite, the answer would be that a physical/digital EQ boost (or decrease) will never result in an actual "flat", mathematically speaking. That said, considering proper approximation, common human hearing capabilities and excluding artefacts in both physical world (see Tartini tones) and digital realm (aliasing issues), there would be no perceivable difference. Commented Jun 10 at 3:51
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    That is incorrect, unless you are assuming that an EQ must be made up of finitely many frequency bands with bandwidth limited to both sides. Also then in digital realm you tend to have a frequency bounded signal. So you are able to work on blocks of finite frequencies. Means there is little you cannot do.
    – Lazy
    Commented Jun 10 at 7:30
  • Alan, I'm confused - your example image is not a straight line at all? So no, that is not at all "the same as just increasing volume". Note that the differences in heights between the six white points a INCREDIBLY LARGE, by eye as much as a decibel or so!
    – Fattie
    Commented Jun 10 at 12:38

2 Answers 2

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The answer is as always: It depends. With classic analogue EQs you’d not be free in terms of response curve. Rather you’d have multiple bandfilters combined with pots cutting a part to ground (passive) or amps (active). The flexibility of the EQ would then also depend on the amount of bands as well as the design (e.g. quality of the filters and stuff). But as you cannot models every response clearly here there is a clear difference between boosting all bands or increasing total volume.

Now with digital eqs there is no need for such a simplification. In theory you can apply any resonance curve. But then it depends on the implementation. Spotify here might use some sort of Spline interpolated curve, which of course models offsets without problems, so yes, in this case it should probably work as well if shifted down.

One reason why this preset is boosted over the whole frequency range might be that people tend to confuse loudness with quality. So playing to music a bit louder might lead to an impression of higher quality. Or it might also be that Spotify will automatically take off 12dB or something when using EQ to allow for headroom, so using a generally boosted approach might be closer to the sound without EQ.

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    Presumably a complex EQ would have non-linear effects on the phase of the signal too?
    – gidds
    Commented Jun 10 at 13:14
  • @gidds With analogue EQs definitely. With digital it depends on how you do it. If you do classic convolution with the fourier backtransform of the response curve and you want to keep the back transform real valued, then the response curve might be complex valued, so induce a (still linear) frequency dependent phase shift. But as the constant curve transforms to a delta at 0 a general gain over the whole spectrum will not induce phase shift.
    – Lazy
    Commented Jun 10 at 15:46
  • Thanks a lot for the answer! I don't think I fully understand though; is there somewhere where I can read about analogue/digital EQs? About the point made in your last paragraph, suppose that you use the acoustic EQ, but then decrease the total volume so that the volume is the same as the flat EQ. Then, the loudness aspect wouldn't make a difference? So I'm a little confused why every frequency range is boosted; it doesn't really make sense why one should ever want to boost every frequency by some amount; my intuition is that if you shift everything down it should be the same
    – Alan Chung
    Commented Jun 10 at 18:51
  • Maybe it's that if you shift everything down, the ratios get a little screwed up?
    – Alan Chung
    Commented Jun 10 at 18:51
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Lazy's answer has it but I can see from the comments there is still some confusion so I'll try address that;

Given that;

  • The eq line is completely flat at some point either above or below the baseline (it's isn't in your picture, but if we assume it is a completely flat line).

  • The graphical representation of the eq applied in the picture from Spotify (or other eq) can be 100% believed (eg. it's not an approximation, it can be considered a scientific graph of output compared to input)

  • The 'circuit' (or digital logical signal path) has the necessary headroom to accommodate such a boost, that is you are not pushing the signal beyond what it's current signal path can support (ie it's not distorting), or a cut is not so large as to drop the signal into the realm of noise and other non-linearities

  • The way the circuit has been implemented does not impart phase shift to any frequency components different to any other frequency components.

Then yes, the input signal will have just been boosted or cut in volume (a gain change of the original signal here) and it should be an identical signal, scaled by the value you boosted or cut each frequency by.

You are correct that there is no point in doing this, you could achieve the same with a gain plugin or change of a fader. If all the above conditions are met it's also true that there would be no real harm in doing it this way either, it would just be a bit of a complicated way to achieve something simple. Yes if you shifted everything down after completely flat boosting it would be as if nothing happened.

So for the theory of what an EQ is and what it does, this might be enough for you, a boost at all frequencies equally is just an increase in volume.

However it's very likely the picture of the eq curve you posted, or similar, is an approximation and the actual eq response is a little more complex, so you may hear a difference, potentially even with a good software eq rather than the Spotify one (though they would probably be fairly close).

Similarly as Gidds pointed out eq changes will shift the phase of frequencies across the spectrum in a complex way. In digital it could be that in the interest of processing speed the eq identifies what in the message signal will change and if nothing, do nothing and no phase shift will be applied. Or it processes very rigorously and whilst using a lot of processing power reaches the same conclusion once processing every frequency, meaning again the output is identical to the input (but boosted/cut)

Or it could have been implemented in a different way where 5 eq bands together create a theoretical 'flat' boost, but each cause phase differences of ±90˚ about it's central frequency (with the progressive change in phase from 90˚ to -90˚ or visa versa about it's centre frequency). In this case the end result is the same as the original but with different phase at different frequencies. This might be hard to notice, and if the implementation was a suitably 'pure' representation of the maths you'd end up with an identical, yet boosted, signal. Or it may be that all the same frequency components are still present just at different phases, and possibly some cancellation may occur between bands and it may not be EXACTLY the same.

Or you could be using a linear phase eq, where no phase shift will occur (at the price of increased processing power) in which case it should be pretty much identical to the original if uniformly boosting all frequencies.

In the analog realm, or in eq's that model the analog realm it is much less likely you will be able to create a completely flat response from, say, 5 bands of eq. You could fiddle for hours and not quite get a flat response, but as you say there's not much point in this so they haven't been designed to make this possible.

Don't worry too much about the phase stuff and so on, or any of the stuff after the bullit points really. Your basic premise that a boost or cut of all frequencies by the same amount is basically an increase or decrease in gain is true, more or less, from my estimation of your level from your question. For the most part the takeaway is if you are boosting the highs, mids and lows with fairly broad eq's then for listening you are not doing much useful, and for mixing a recording you are fundamentally missing the point of mixing and just boosting a part, potentially with some small variation.

Occasionally you may see techniques such as using an EQP-1A low band to boost at 60Hz and cut using the mid band at 100Hz (if memory serves, a while since I was using one regularly!) which may seem counterintuitive, but is really just taking advantages of non-linearities in those two bands to end up with a composite eq curve not possible with one band alone. This is not creating a flat response, the way the two bands are designed means you get something new by boosting then cutting, worth knowing but doesn't effect your fundamental hypothesis.

As other have alluded to, it gets a lot more complex if you want to get the scientific answer, though arguably the basic hypothesis is roughly true for the average music listener or for home recording. Most professional recording engineers wouldn't know much of the technical details either, but would work with the assumption that a uniform flat boost or cut would probably change the signal a tiny bit, though potentially barely noticeable.

If you want to know more about eq design and function it is a little mathematical, you could look into first order RC and RL filters, then second order+, and their transfer functions to learn about how they do what they do and how they shift phase about. Then looking into software implementations of the same thing and how they may or may not mimic their real world counterparts!

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