The limits of EQ

Why Can't I Fix All my Acoustic Problems with EQ?

This topic deals with an important question: why isn't EQ enough to sort out acoustic problems? There are plenty of products that claim to be able to correct room responses, so why would anyone need to bother with acoustic treatments and bass traps and absorbers and all that stuff? Technology to the rescue, right?

Those are important questions, and understanding the answers to them can help a lot with better understanding acoustics in general. There are a few places where the answer gets a little technical, but for the most part the explanation is fairly easy to follow. Along the way to answering the questions above, we will touch on the answers to two other questions:

Why does phase matter?

Why should I look at time domain signals instead of just frequency responses?

What does EQ do?

As a starting point we need to take a look at what an equaliser can do for us. The basic function of an equaliser is to alter the frequency response. We can use it to try and make all the frequencies in the response equal - the clue is definitely in the name there! Particular equalisers are sometimes described as operating in the frequency domain, or operating in the time domain, or operating in both. In fact all equalisers, without exception, operate in the time and frequency domains and have effects in both.

What are the limits of applying EQ?

Location, location, location

Before we start adjusting an EQ to alter the frequency response, we need to see a response to adjust, so we need to make a measurement. This brings up the first limitation. The measurement is made at a single position, and the frequency response of that measurement is only valid at that position, moving the mic elsewhere and making another measurement will produce a different frequency response. It may be a little different, or it may be (and usually is) a lot different. The changes made by an equaliser in the path to the speaker are the same no matter where we are in the room, so since the response is changing in different positions and the EQ isn't, it stands to reason that the EQ is only going to be good in places where the frequency response is the same as the one we used when setting the EQ.

Reading some of the advertising blurb for EQ products you could be forgiven for thinking that some clever guys somewhere have figured out a way around this. They haven't. The best you can do is to look at the frequency responses measured at many positions in the area where you need the correction to work, figure out which bits of them are sufficiently common, and come up with a compromise EQ setting that helps somewhat in most places and doesn't do too much harm elsewhere. It can help, but it is no magic bullet.

What if I only listen in one spot?

So if the EQ is only good for one position, and I only sit in one position, what's the problem? The problem is very small movements make big differences. At high frequencies the wavelength of sound is very short. At 20kHz it is just 17mm, about 5/8". The frequency response varies dramatically at high frequencies over very short distances, so even if you only sit in one spot, and sit very still, the best you could hope for is an EQ setting that would work up to a few kHz. For a more reasonable range of motion a few hundred Hz is more likely.

Resolution

So we are prepared to make some compromises. One sweet spot will do, and fixing the response up to a few hundred Hz would actually help a lot, it's usually all over the place down low. So let's break out the EQ and start adjusting. The next problem we run into is the adjustments don't seem to be working right. Say the frequency response shows a 6dB dip at 100Hz. We put in 6bB of boost there and tweak the width so it matches the dip we saw. But the frequency response hardly moved, especially in the middle of the dip. What's going on? The problem is probably with the resolution of the measurement. If you have used a 1/3 octave RTA, for example, to measure the response, the bar at 100Hz actually spans the range from about 89Hz to 112Hz. That 6dB dip is probably due to a much deeper but very narrow dip within that 23Hz span. You have to make a high resolution measurement to see what is going on, an RTA isn't going to cut it for this work.

Headroom

The RTA has left the scene and we are making high resolution measurements. And they look awful. There are big peaks and some huge, narrow dips. The 6dB dip we saw at 100Hz actually turns out to be a 17dB dip at 98Hz. Never mind, the EQ allows up to 24dB gain. But listening with the fix in place reveals massive distortion. We have run right out of headroom, with clipping all over the place. Even after playing around with the levels to get rid of the clipping the result even slightly out of the sweet spot is much, much worse. Sharp dips in the response are very sensitive to position, even at very low frequencies. The sensitivity to position and the headroom problems mean we cannot do anything about them with EQ. The best we can do is deal with the broad, shallow dips and work on the peaks.

Minimum phase and all that

We know most of the limitations of the equaliser now. We moved things around a bit and used a few absorbers and got rid of the worst of the dips. After a lot of painstaking tweaking of the EQ the frequency response is actually pretty flat. But it still sounds awful. So now what is going on?

The next few paragraphs get a little more technical, but it is worth sticking with it. Equalisers are, with a few exceptions, minimum phase devices (some are linear phase, but that doesn't help with the problem facing us). When we make an adjustment to the frequency response on the EQ, we also change the phase response, an often ignored part of the measurement we made. We need to take a short diversion to look at why we should care about the phase.

Why does phase matter?

Measurement software measures the Transfer Function of the system it is hooked up to. The transfer function has two parts, the familiar frequency response, and the phase response. Systems can have the same frequency response but actually have totally different effects on signals passed through them - the difference lies in their phase responses. As a simple example of how big a difference phase can make, consider the results from measuring two very different signals: an impulse and a period of periodic noise. Both of these signals have perfectly flat frequency responses, looking at the frequency responses we could not tell them apart. The time signals obviously look completely different, so what happened to that difference when the signal went through an FFT to make the frequency response? It is all in the phase responses. The impulse has zero phase at all frequencies. The periodic noise has random phase. Just as looking at frequency response alone cannot tell us what a signal looks like, looking at the frequency response of a transfer function alone cannot tell us what the system does to signals that pass through it, we have to look at the phase response as well.

So the answer to why our system, with its nicely flattened frequency response, still doesn't sound right lies in the phase response. Room responses are, for the most part, not minimum phase. The technical explanation of that probably would not help with our understanding of the problem we are faced with, but the outcome is this: we can do almost what we like with the frequency response (within the limits we have discussed already) but the phase response is beyond the reach of our EQ. Anything we do in the EQ's frequency response adjustments will have a corresponding effect in the phase response, and while the frequency response adjustment we make can be equal and opposite to the room's frequency response, the same is not true of the phase. That is what it means for the room not to be minimum phase, it has done things to the phase of the signal that we cannot mirror in our EQ. Fixing the frequency response but not the phase response means we cannot make the time signal look like it did before the room got hold of it, however much time we spend fiddling with the EQ. We have hit the limit.

The value of looking at time signals

That brings us to another item I said we would touch on, the value of looking at time signals and not just at frequency responses. The frequency response is only half of the description of what the system is doing to signals that pass through it, the phase response is the other half. Trying to understand systems by looking at the frequency response alone is like trying to understand a book by reading only the even numbered pages. To really understand you need to look at both. That is a bit problematic, however. The frequency response is fairly easy to understand, but the phase response doesn't give up its secrets quite so easily. To properly use it we end up looking at various quantities derived from it, such as group delay or phase delay. It gets complicated. But there is an alternative.

The systems we measure can be described in two ways: in the frequency domain by their transfer function (frequency and phase responses) or in the time domain by their impulse response. They are two views of the same system, the transfer function is the FFT of the impulse response and the impulse response is the inverse FFT of the transfer function. To study how the system behaves and what it does to signals, we can look at both. The impulse response has the benefit that it captures all the information in one signal, which puts it one up on the transfer function, though it is not as immediately intuitive as a frequency response. It readily gives up information that is less easily spotted in the transfer function though, such as early reflections or the slow decays of room modes. It is well worth taking some time to become familiar with the impulse response and some of the quantities derived from it, such as the impulse response envelope (aka ETC).

Does EQ help or not?

Given all the limitations we have uncovered, and with the problem of non-minimum phase on top, we might wonder whether the equaliser is any good to us. All is not lost, however. The non-minimum phase behaviour of the room is connected to the dips in the response. It means we are even less able to deal with them, but there wasn't a lot we could do about them anyway, so we are really not much worse off. On the plus side, the peaks of the response are caused by features that lie firmly in the region our minimum phase equaliser can handle. We can use the equaliser to help tame the peaks, and the lower down they occur, the better the results we are likely to get - a nice complement to our acoustic treatments, since they start to struggle (or we start to struggle with the size of them!) at low frequencies. EQ is a useful tool to keep handy when trying to fix our acoustical problems, but it can only ever be a small part of the solution.