The WavePurity Reverb Processor

General Information

Reverb is derived from the word "reverberate", which means to resound or re-echo. Reverb filters create a stereo sound and are able to mix this with the original sound. To the listener, this creates the illusion of a concert hall.
Many modern sound cards offer the possibility to create reverb effects. Very often, the quality of the digital signal processors they use is considerable. There is, however, one basic problem: The effects of the sound card cannot be used for direct digital signal processing. Duplex sound cards, which can record and replay simultaneously, allow you to replay a track with the use of effects and to re-record it at the same time.

WavePurity creates the reverb effect by using a software algorithm , and this allows you to edit wave files directly. The implementation of the WavePurity reverb effect algorithm is based on a scientific publication of the

Institute of Technology, Cambridge, Massachusetts
"The Virtual Acoustic Room", 1982
by William Grant Gardner, Master of Science

In this publication, William Grant Gardner deals in great detail with the acoustic reproduction of rooms by the use of all-pass filter systems. He examines ways of implementing these filter systems through the use of digital software algorithms. For example, by implementing three filter systems, he demonstrates the simulation of small, medium-sized and large rooms. The resulting sound patterns are based on the "classroom", "auditorium" and "concert hall".

These three software algorithms "small room", "auditorium" and "concert hall" have been implemented in WavePurity. They can be used to create a stereo effect for otherwise dry-sounding recordings.

The implementation of the algorithm through the use of all-pass systems allows you to apply the filter in real-time , which means that, even while a music track is being transmitted to your sound card, WavePurity still has plenty of time to first pass all data points through the reverb filter. Please note that this feature requires a CPU with a minimum clock rate of 400 MHz, if you want to create a stereo reverb sound in real-time.

Operating principle of the WavePurity reverb filter

In the explanations of the following section, some excerpts from the scientific publication by William Grant Gardner will be presented.

1. Acoustic simulation of a room in the digital world

If you are in a room, for example in a large concert hall, a spoken word, a sound or a tone will reach you directly through the air, but at the same time it will also be reflected towards you in many ways by echoing from the walls, the ceiling, and from objects within the room. This causes multiple reflections, which you will usually perceive as the slowly fading echo of a sound. At the same time, the air in the room transmits low frequencies more easily than high frequencies. Think of an open air concert, where the low bass sound of the loudspeakers can be heard from a great distance, but not the high-frequency details. In consequence, a fading sound in a concert hall also seems to become lower. For example, you can hear this effect very distinctly inside a church. Up to now, we have discovered two very important characteristics:

.The sound inside a room is made up of a large number of individual reflections of the signal source.

.In addition, the reverberation inside a room is absorbed through the air, which creates a damping effect for higher frequencies over time.

In the digital world, theoretically, we can do the following:
We need a significant signal source which emits a sound that should be as short and precise as possible. Think of the sound of clapping hands in a large hall. Technically, this signal source is called a Dirac function or pulse function. Readers with some knowledge in communications engineering may be reminded of electrical signal systems. In those systems, it is known that the system behavior of an electrical assembly, such as, for example, its frequency response, can be tested by using an impulse generator. It works just the same in acoustics. If we manage to record digitally the signal of a short sound impulse in a concert hall and to include the entire reverberation, which may last for several seconds, we will know everything about the acoustical properties of that room.

At the top left, you can see the signal impulse, and on the right, the sound characteristics recorded in the room. Now, there is a theoretical trick which allows us to apply the characteristics of this room precisely to a dry-sounding music track, thereby creating a sound as if the music had been played in this very concert hall. This trick is known as "convolution". To apply it, we need a "fifo", namely a "first in first out" shift register, through which we push the incoming digital data points of the music track. The fifo register must have exactly the same length as the sound signal from the concert hall. In each step, we carry out a multiplication of each fifo register position with the corresponding data point of the sound signal, and then sum up all the results. By this "convolution", the acoustic characteristics of the concert hall are precisely imprinted upon the music track. As a result of every step, we get the reverb signal of the concert hall for this particular data point. This is the theory. If you have several days to wait for the result, this is the right method to use. In practice, however, this method would be much too slow, even if today's super-fast processors were used, and you could never apply it in real-time: for example, for a reverberation time of three seconds and a data rate of 44.1 kHz for every sample, you would have to carry out 132300 multiplications and summations. This would amount to 132300 x 44100 = 5.8 billion mathematical operations per second - an impossible task.

Consequently, there have been many attempts at simulating stereo sound by using simple feedback systems. Think of old Karaoke systems, some of which already used mechanical, metallic reverberation generators. From today's point of view, such systems are outdated because of their low quality and their large size. Today, small DSPs (digital signal processors) are used instead. Their architecture is designed exactly for the simulation of particular effects. Nearly every sound card today is equipped with such a module.

However, there is also a second method: Stereo sound can also be simulated by using optimized software algorithms. For this method, so-called all-pass filter systems are used: to create a stereo sound, several all-pass filters are combined or even nested. What is an all-pass filter? It is simply a compensated comb filter. Technically, it is simply a delay combined with a feedback, namely a fifo in which the output signal is transmitted back to the input with a particular feedback factor. The WavePurity echo filter, for example, consists of two comb filters.

If the delay period is very short, logically there will be some interferences and phase shifts at certain frequencies. To compensate for this, the original signal is rated with the negative value of the feedback factor and overcoupled from the input to the output. This creates an all-pass filter which compensates for those unwanted effects.

In his publication, William Grant Gardner demonstrates how to build an all-pass by using a relatively simple software algorithm:

This module is applied repeatedly to build a reverb processor. In addition, a low-pass filter is required which, in the feedback branch, simulates the absorption of high frequencies by the air in a room. William Grant Gardner developed three experimental room models, which are very well suited for simulating the reverb effect for rooms of their respective types. In the WavePurity reverb processor, these very models have been implemented:

The diagrams look surprisingly simple - and once they have been determined experimentally, they are indeed easy to implement, use little processing time, and achieve an extremely good simulation of the stereo sound.

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