Dr. David Berners (left) is the Universal Audio Director of Algorithm Development; Dr. Jonathan Abel is the co-founder and CTO

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Drs. David P. Berners and Jonathan S. Abel Answer Your Signal Processing Questions.

About This EMT140 Business
In this month's column, we're going to talk about the physics and the psychoacoustics behind the EMT140 plate reverberator-in particular, what creates its unique sound. We'll also touch on the technology we used to emulate the three plates at The Plant studios in the Plate140.

Configuration
As you may recall if you read in Will Shanks' Analog Obsession column in May 2004, the EMT140 is an incredibly musical reverberator, and one of the first artificial reverb devices manufactured; it was released in 1957. The EMT140 has a pair of large-roughly ping-pong table-sized-vertically mounted plates enclosed in a particle board casing, and usually suspended from the ceiling for mechanical isolation, as seen in Figure 1. One of the plates-the signal plate-is a very thin sheet of steel that is attached at its corners to a tubular frame and held under tension with pairs of rubber tensioners. It is fitted with a driver that vibrates the plate in response to the input, and pick-ups that detect the reverberated output. The second plate-the damping plate-is covered in a packed asbestos and may be positioned closer to, or farther from, the signal plate to control decay time.

Figure 1 (left) and Figure 2

The driver is mounted near the signal plate center and moves the plate in the transverse direction (perpendicular to the plane of the plate) in response to input signals. The plate supports wave propagation, and, a little like throwing pebbles into a swimming pool, waves propagate out from the driver and reflect from the edges. Each reflection, in turn, propagates over the plate, creating more reflections as plate edges are encountered. In this way, the pick-ups "hear" a reverberated input containing thousands of instances of the input signal propagated through different paths across the plate.

“Roughly speaking, humans perceive arrivals within about 20 ms of each other spectrally, as equalization or timbre. Arrivals that are spaced further apart than this often appear temporally, as echoes.”

Wave Propagation
The plate, however, isn't simply a small two-dimensional room: The wave propagation mechanism is different from that of air and gives the EMT140 its unique whip-like onset. It turns out that air, thin strings and membranes all have non-dispersive wave propagation; that is, all frequencies travel at the same speed. This means that traveling waves maintain their shape while propagating. For instance, a wave passing by one point on a thin string or membrane will appear in tact as it passes by other points.

Thin strings and membranes propagate waves via a stretching mechanism, as illustrated in Figure 2. Essentially, in any curved section of a thin string under tension, a restoring force develops, which tends to straighten out the curve. As points on a curve are accelerated, the string stretches, accelerating adjacent points, thus propagating the wave.

Figure 3

As seen in the upper diagram in Figure 2, in structures that are sufficiently thick, such as plates or thick strings, there are a number of forces present that tend to straighten bends in the material. Loosely speaking, where a plate is curved, the material is stretched on the outside of the curve and compressed on the inside of the curve, resulting in forces tending to straighten the bend. In this way, plates support wave propagation, though clearly the mechanism is different from that of a thin string or membrane.

For those interested in the details of wave propagation on membranes and plates, we recommend visiting Stanford professor Julius Smith's CCRMA Website and reading these articles:

• Ideal Vibrating String
• The Stiff String
  

For our purposes, what's important is that (for the small-amplitude vibrations induced by the driver) the plate is linear but dispersive, with a high propagation velocity. By linearity, we mean that the plate's response to a sum of signals is the sum of the plate responses to the signals individually. That the plate is dispersive means that different frequencies travel on the plate at different speeds. On a plate, high frequencies outrun low frequencies, and injected transverse waves don't keep their shape. In some sense, a plate may be thought of as a sequence of membranes, each propagating a different frequency band and each sized according to the propagation velocity in that band.

Several features set the EMT140 onset apart from that of typical room reverberation: The EMT140 onset is very abrupt in energy and echo density, and has what some describe as a "whip-like" character. Roughly speaking, humans perceive arrivals within about 20 ms of each other spectrally, as equalization or timbre. Arrivals that are spaced further apart than this often appear temporally, as echoes. The fast propagation velocity of the plate results in a great many echoes arriving at the pick up within the first 20 ms. This initial set of arrivals conveys a sense of immediate onset-both in energy and echo density. Because the high frequencies arrive first, there is an evolving equalization at the very beginning of the onset, which we believe is responsible for the "whip-like" sound.

Damping
Signals propagating on the plate decay through a number of mechanisms. Bending and stretching of the material results in thermoviscous losses in the steel, which preferentially absorb high frequencies. This absorption of high frequencies is similar to that in large spaces, where air absorption dominates the high-frequency decay rates.

The tensioners holding the signal plate to the corners of the frame are also lossy. The tension and tensioner damping determine the losses, and in turn the reduction in decay time as a function of frequency. It seems that a lot of the plate-to-plate variation is due to the tensioners.

As the plate vibrates, it moves the air around it, and in doing so, radiates away energy that would otherwise remain circulating in the plate. Air weighs about a kilogram per cubic meter (kind of heavy, when you think about it), and the plate has a surface area of around five square meters. Low-frequency vibrations can move the plate a decent fraction of a centimeter many times each second, so it's not hard to see that radiation losses can limit the low-frequency decay times.

When the damping plate is placed near the signal plate (but not touching it), there is only a thin channel around the edges of the signal and damping plates where air can move in and out in response to signal plate motion. This exaggerates the effect of radiation losses, causing the low frequencies to decay rather quickly when the damping plate is close to the signal plate.

Figure 3 shows power as a function of time (on the vertical axis) and frequency (on the horizontal axis) for five different damping settings. Note that the high frequencies decay at a fairly constant rate, irrespective of the damping plate position. The low frequencies, on the other hand, vanish rapidly when the damping plate is close to the signal plate.

Modeling
In theory, the EMT140 is approximately linear and time invariant (LTI), and one of the first things we did in trying to figure out how to model the EMT140 was to test this assumption on the plates at The Plant. The idea was that a linear, time-invariant system is completely characterized by its impulse response-its response to any input is that input convolved with its impulse response. So, to model such a system, it isn't necessary to make a physical model of all system components and their interactions. This kind of model is necessary for compressors, for example, where the behavior of the device depends on the input signal. By making a physical model, you can be reasonably comfortable that your model will behave appropriately for most any input signal.

Linear, time-invariant systems do the same "computation," regardless of the input. So, if the plate were LTI, it would be sufficient to develop a linear, time-invariant system that reproduces the psychoacoustically relevant impulse response features. Having done that, we could be confident that it would be an accurate model for any input.

It turns out that, at levels typically used in the studio, the plates appeared pretty close to LTI. Given this fact, we measured the plate impulse responses at a number of damping settings for each of the plates modeled. At the same time, based on the physics of the plate, we developed parametric models describing important impulse response features as a function of the damping plate position. We then fit these model parameters to the measured impulse responses using analytical methods, and hand tuned them while listening to a range of source material.

The advantage of using a small number of physical parameters to define the system behavior is that, by selecting the parameters to give a good match to the measured impulse response at just a few damping settings, a good match is achieved over the entire range of damping settings. Indeed, our listening tests at The Plant confirmed an excellent match to each plate over its entire damping setting range.

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