# Convolution reverb

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Convolution reverb

In audio signal processing, convolution reverb is a process for digitally simulating the reverberation of a physical or virtual space. It is based on the mathematical convolution operation, and uses a pre-recorded audio sample of the impulse response of the space being modelled. To apply the reverberation effect, the impulse-response recording is first stored in a digital signal-processing system. This is then convolved with the incoming audio signal to be processed. The process of convolution multiplies each sample of the audio to be processed (reverberated) with the samples in the impulse response file.

## Creation of impulse responses

An impulse response is a recording of the reverberation that is caused by an acoustic space when an ideal impulse is played. However, an ideal impulse is a mathematical construct, and cannot exist in reality, as it would have to be infinitesimally narrow in time. Therefore, approximations have to be used: the sound of an electric spark, starter pistol shot or the bursting of a balloon, for instance. A recording of this approximated ideal impulse may be used directly as an impulse response. Techniques involving starter pistols and balloons are sometimes referred to as transient methods, and the response is contained at the beginning of the recording in an impulse.

Another technique, referred to as the sine sweep method, covers the entire audible frequency range, which can result in a broader-range, and higher-quality, impulse response. This involves the use of a longer sound to excite a space (typically a sine sweep), which is then put through a process of deconvolution to produce an impulse response. This approach has the advantage that such sounds are less susceptible to distortion; however, it requires more sophisticated processing to produce a usable impulse response.

A third approach involves using maximum-length sequences, but this is difficult in practice because such sequences are highly susceptible to distortion.

The impulse response of a system is equal to the inverse Fourier Transform of the cross-correlation of the output of the system with the auto-correlation of the input to the system. For example, to sample the acoustic properties of a larger space such as a small church or cathedral, the space can simply be excited using white noise, with the result recorded both near the source, and somewhere else in the space. The coefficients of a finite impulse response can then be generated using the mathematical approach mentioned above.

## Applications

### Real space simulation

The primary goal of a convolution reverb is to sample real spaces, in order to simulate the acoustics of the sampled space. A straightforward and simple mono example of capturing an impulse response would be to set up a microphone in a concert hall and to place the microphone in the centre of the auditorium. Next, produce a very brief pulse (often an electric spark) of sound, and record everything that the microphone picks up, which includes both the original sound and the response of the room to it. The recorded take would then be cleanly edited and loaded into the convolution processor. This convolution can be applied as part of a signal processing chain.

### Machine simulation

It is also possible to sample the impulse response of a reverberation unit, instead of sampling a real space. Thus, it is possible to use a convolution reverb in place of a hardware machine. The techniques used to sample a reverberation unit are the same as the ones used to sample real spaces.

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