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Understanding Natural And Digital Reverb

Editors note: This article was originally published in 1997, but the information is still relevant today. You can read and comment on the original article here.

Reverb is one of the most interesting aspects of digital signal processing effects for audio. It is a form of processing that is well-suited to digital processing, while being completely impractical with analog electronics. Because of this, digital signal processing has had a profound affect on our ability to place elements of our music into different “spaces.”

Before digital processing, reverb was created by using transducers—a speaker and a microphone, essentially—at two ends of a physical delay element. That delay element was typically a set of metal springs, a suspended metal plate, or an actual room.The physical delay element offered little variation in the control of the reverb sound. And these reverb “spaces” weren’t very portable; spring reverb was the only practically portable—and generally affordable—option, but they were the least acceptable in terms of sound.

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This article is provided by EarLevel Engineering.

First a quick look at what reverb is: Natural reverberation is the result of sound reflecting off surfaces in a confined space. Sound emanates from its source at 1100 feet per second, and strikes wall surfaces, reflecting off them at various angles. Some of these reflections meet your ears immediately (“early reflections”), while others continue to bounce off other surfaces until meeting your ears. Hard and massive surfaces—concrete walls, for instance—reflect the sound with modest attenuation, while softer surfaces absorb much of the sound, especially the high frequency components. The combination of room size, complexity and angle of the walls and room contents, and the density of the surfaces dictate the room’s “sound.”

In the digital domain, raw delay time is limited only by available memory, and the number of reflections and simulation of frequency-dependent effects (filtering) are limited only by processing speed.

Two Possible Approaches To Simulating Reverb

Let’s look at two possible approaches to simulating reverb digitally. First, the brute-force approach.

Reverb is a time-invariant effect. This means that it doesn’t matter when you play a note—you’ll still get the same resulting reverberation. (Contrast this to a time-variant effect such as flanging, where the output sound depends on the note’s relationship to the flanging sweep.)

Time-invariant systems can be completely characterized by their impulse response. Have you ever gone into a large empty room—a gym or hall—and listened to its characteristic sound? You probably made a short sound—a single handclap works great—then listened as the reverberation tapered off. If so, you were listening to the room’s impulse response.

The impulse response tells everything about the room. That single handclap tells you immediately how intense the reverberation is and how long it takes to dies out, and whether the room sounds “good.” Not only is it easy for your ears to categorize the room based on the impulse response, but we can perform sophisticated signal analysis on a recording of the resulting reverberation as well. Indeed, the impulse response tells all.

The reason this works is that an impulse is, in its ideal form, an instantaneous sound that carries equal energy at all frequencies. What comes back, in the form of reverberation, is the room’s response to that instantaneous, all-frequency burst.

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An impulse and its response

In the real world, the handclap—or a popping balloon, an exploding firecracker, or the snap of an electric arc—serves as the impulse. If you digitize the resulting room response and look at it in a sound-editing program, it looks like decaying noise. After some density build-up at the beginning, it decays smoothly toward zero. In fact, smoother sounding rooms show a smoother decay.

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