Read the first part of this article here.

DSP and Phase Correction

The point I was trying to make in Part 1 regarding amplifiers also holds true for DACs. Where 10 years ago I built discrete DACs, the latest batch of chips truly sounds good enough to be used in any stratum. This makes moving filtering and processing into the digital domain an obvious choice from both a performance and cost perspective. It also enables types of signal processing that are impossible to do in the analogue domain.

In all the multiway examples referenced in Part 1, the leading edge of a transient—meaning the high frequencies—was reproduced immediately, while the lower frequencies come slightly later. This is because to design a low pass filter—a filter to allow low frequencies to pass through while blocking or reducing high frequencies—you need to find a trend in the signal. You need to let some time pass to observe the signal before you see such a trend. High pass filtering also needs to find a trend, if only to remove it from the signal. In both cases, high frequencies come out right away and low frequencies get delayed. Unless you are clairvoyant, you can’t undo this delay.

The only alternative is to delay the high frequencies so that they align with the delayed low frequencies, effectively reassembling the original impulse. That entails somehow keeping the high frequency waveform in store until the right moment. It’s a task absolutely tailor made for DSP. Memorizing stuff is what digital does.

The brilliant thing about digital filters is that you can make them with any impulse response imagineable. How about one where the high-frequency part of the signal comes last?

That’s precisely how you do it. Your speaker’s response includes unwanted all-pass behavior, meaning all frequencies pass through but with phase shifts. To fix this, take the impulse response of the unwanted all-pass filter, reverse it in time, and create a digital filter based on this reversed response. Then, place this new filter before the crossover filter. It’s really that simple.

Here’s the actual, measured step response of a DSP controlled four-way speaker:

It’s a dead ringer for the one-way example I gave in Part 1, except that this speaker is physically possible and otherwise has all the advantages of a multiway system.

What boggles the mind is that on the audio opinion circuit, people are locked in mortal combat over the question of whether a PCM signal causes “time smear.” They’re fighting over microsecond-level subtleties in the impulse response of a digital converter, while the gross time distortions caused by passive speakers get completely ignored. Established engineering principles like distortion testing and negative feedback are loudly pooh-poohed, while the one truly questionable bit of schoolbook wisdom, the supposed inaudibility of phase shifts, is parroted as gospel. Why? Answer: To keep that infernal cycle of equipment upgrades and trade-ins going, that’s why!

It’s more lucrative to misdirect customers’ attentions to smallish differences between sources, amplifiers and wiring, and to foster a market that welcomes flawed electronics to provide those differences. This whole house of cards relies on passive speakers.

Speakers in Rooms

Making a hi-fi speaker work in a room is considered black art. You shuffle speakers, sofas and other furniture around for days to make things sound as right as you can make them. Except this does nothing to mitigate reverberations per se: the room still rumbles after a bass transient. All you can hope for is that no frequency band is disproportionately affected. In the time domain, that means you’re trying to spread out the arrival of the echoes as randomly as you can.

Put simply: when you arrange the speakers and the listener where the 1/3^rd octave smoothed response looks flattest, the transient response is guaranteed to be the most chaotic.

When the bass is uneven and bloated, we tend to blame the room. After all, dropping another speaker in the same spot usually causes the same problems. That doesn’t mean you can’t design a speaker that interacts better with the room. It only means that it’s not often done.

Causes of the Room Boom

A driver on the front behaves very differently at high and low frequencies. High-frequency sound is launched only into the half of the room that can “see” the driver. Low-frequency sound waves, i.e., those whose wavelength is long compared to the width of the cabinet, just bend around it. If you turn a speaker away from you, the top end disappears but the bass stays the same.

Because high frequencies are radiated into half the space that bass frequencies are, the anechoic frequency response ramps up by about 6 dB—or, viewed another way, the bass appears 6 dB lower. This shift is why the transition point between full-space (bass) and half-space (treble) radiation is often called the “baffle step frequency.”

Now, speakers are designed to have a flat anechoic frequency response. To do this, designers often build in a 6 dB bass boost to compensate for the baffle step, and in the process quadruple the amount of bass power that goes into the room. But it’s exactly in the bass where room problems are hardest to fix! Splashy highs are nothing that a bit of extra upholstery or soft furnishings won’t put right. But bass problems? Oh dear.

Unless you somehow get rid of the energy that the speaker radiates away from the listener, it will start bouncing around the room. That’s why, when people add acoustic absorption, most of it gets placed behind the speakers—it’s the first place to control those early reflections.

The term “baffle step correction” is clever framing—it makes an added problem sound like a solved one. It has the ring of some advanced speaker design technique, but it’s really a way for designers to wash their hands of the whole knotty issue.

Directivity Control

I need to pause for a second and note that directional bass is not the sole province of active speakers. For example, a straightforward dipole emits much less unwanted power and tends to produce a much leaner, punchier bass in most spaces. Passive cardioid speakers exist too—the Finnish company Gradient has been making them forever. If the company is relatively unknown, that’s only because it was ahead of its time.

But it’s certainly true that active speakers have launched the idea of directivity control into the public consciousness. 2015 saw the launch of at least three notable products in that regard.

Bang & Olufsen’s Beolab 90 uses an impressive number of drivers to provide digitally adjustable directivity:

My own Kii THREE speaker digitally overlaps the frequency ranges of two sets of woofers and the midrange driver to create a unidirectional (cardioid) output starting from the upper bass frequencies. Below 50 Hz, all woofers operate in phase as a monopole (i.e., omnidirectional):

The Dutch & Dutch 8c speaker employs a midrange cardioid passively using a large midrange driver with side vents and adds an omnidirectional subwoofer on the back of the speaker to take over frequencies below 100 Hz:

Although the Kii THREE (along with its smaller successor, the SEVEN) and the Dutch & Dutch 8C control directivity using very different methods, they share the same underlying philosophy: both speakers behave as half-space radiators down to much lower frequencies than similarly sized conventional cabinets—but not all the way down. A transition frequency still exists, but it is deliberately lowered.

Here’s the clever bit: no 6dB low-frequency boost is added. Anechoic measurements show the bass response is 6dB lower than flat. The user, however, is expressly told to back the speaker against the wall. Thanks to the lowered transition frequency, the rearward bass energy—reflected off the wall—is still in phase with the forward output, effectively restoring the missing 6dB. Above the transition frequency the speaker is unidirectional, so the wall is out of the equation entirely. Result: the direct sound has a perfectly flat bass response while the reverberant field is 6dB quieter. That’s enough difference to turn a “bad” space into a workable one and a good space into an incredible one. In a room that previously killed half of the bass notes and let others rumble on interminably, you can suddenly follow the bass line, with notes starting and stopping when they should.

Conventional speakers won’t let you do that because the transition frequency is too high. You get severe comb filtering unless you either pull the speaker out into the room or fit it into a hole in the wall, like they do in studios. The point of lowering the transition frequency relative to the size of the box is to get in-wall-like behaviour without the hole.

Inspired by the success of these products, one manufacturer of plate amplifiers (ready-built active speaker electronics that bolt into a compartment in the cabinet) now includes directivity control as standard in its DSP tool set. As it relies specifically on woofers on the front and back of the cabinet, the resulting directivity is not a perfect cardioid but it’s still much better than not controlling directivity at all.

Integration

Today’s general-purpose CPUs have more computational power than you’ll ever need for an active speaker. So, just as hi-fi dealers were slowly coming around to the idea that a modern audio system might consist of nothing more than a streamer and a pair of active speakers, loudspeaker manufacturers have begun including the streamer function for free. All you would need to get these speakers going is a Wi-Fi network and AC power.

The Kii SEVEN (above) and KEF LS50 (below) are just two examples of active speakers with built-in Wi-Fi and streaming.

This presents a serious challenge commercially. Hi-fi dealers often take on an active speaker line because they genuinely love the sound—only to discover that recommending it to an existing customer could cost them a sale. A typical hi-fi transaction might consist of selling, say, a DAC and taking the customer’s old one in part exchange, to resell second-hand.

So when a customer walks in looking to spend $10,000 on a DAC, it takes remarkable honesty for a dealer to admit that, for the same money, they could get a pair of active speakers that would run circles around their entire $100,000 passive system. And so, active speakers languish in a corner, waiting for that one customer with no existing hi-fi system who suddenly decides to shell out ten grand to get one. Doesn’t sound too likely, does it?

And if any dealers are reading, here’s a tip: the customer who buys an expensive pair of active speakers is probably upgrading from a cheaper pair. Make sure you’re the one who sold them those.

Caveat Emptor

Before you run and buy a pair of active speakers, a word of caution. Just because fantastic active speakers exist today doesn’t mean that all active speakers are suddenly great. Many are still no more than dressed-up passive speakers. Ported cabinets are so ingrained in speaker design that many active speakers use them too, without their designers realizing that they’re wasting an opportunity for improvement. And even if there’s DSP inside, that doesn’t mean it’s being used for more than basic EQ adjustments. Phase correction is not universal, directivity control even less so. The key point is these things are now possible. Active speakers hold all the cards to trounce passive ones—but only those that have played their hand well do so.

Summing Up

We’ve identified several techniques that become possible when a speaker is made active—many of which improve transient response across different frequency ranges, for different reasons:

• Sealed cabinets become viable, delivering tighter, more tuneful bass.
• DSP can correct the phase shifts introduced by crossover filters, yielding an electrostat-like transient response out of a multiway speaker. The sound becomes extraordinarily light on its feet, with more precise timing and more powerful “slam”—all at once.
• Directivity control mitigates the influence of room acoustics. Bass and lower midrange become much more highly resolved.

The remaining benefits contribute to a smaller, more practical design that more people can use and enjoy.