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Convolution: crunching the numbers

Convolution: crunching the numbers

Around the turn of the century, convolution started to become reality when three companies brought out sampling reverberators to the market: Audio Ease, Yamaha, and Sony.

Audio convolution means calculating the flow of an audio signal through an audio impulse response – a “sample”, in order to recreate the process using a digital algorithm. The most appealing example is the application of convolution reverberation, also known as ‘sampling reverb’. Basically, a signal is fed through a series of delays and attenuators – very similar to an FIR filter, with all delay times and levels representing the room’s impulse response. In fact, a convolution algorithm and an FIR filter are the same thing, with the FIR filter consisting of a dozen to a few hundred taps (delay & attenuator), and a reverberator consisting of more than a hundred thousand. Straight convolution is a particularly DSP-hungry process… compared to a simple PEQ, delay and level process in a DSP system, convolution needs thousands times more DSP power.

When the Apple G4 computers were introduced in 2000, the Dutch company Audio Ease discovered that the AltiVec arithmetic core of the G4 processor, put there by Apple and IBM to support complex vector calculations, could support also very processor-efficient Fast Fourier Transformation (“FFT”). This allowed an 800Mhz Apple G4 computer to be able to transform audio streams from the time domain to the frequency domain and back . The trick is that applying convolution in the frequency domain is easier than in the time domain – allowing a computer that was hopelessly slow at today’s standards to perform convolution reverberation in real time ! They called their invention Altiverb, paying homage to the AltiVec engine in the Apple/IBM G4 processor.

Sony used a similar concept in hardware with the DRE-S777 ‘triple seven’ machine, using FFT to perform convolution in the frequency domain.

Yamaha took the straight approach and went the difficult route, building the SREV1 sampling reverb, a 3U 19” frame hosting a huge number-crunching machine with 32 DSP cores to do the tough job of processing two channels of 5,4 seconds reverberation, or 4 channels of 2,7 seconds. Mounting an optional DSP board added 32 more dedicated DSP cores for the convolution, doubling the reverberation times. All in the time domain, no FFT going on. The DSP capacity of the SREV1 ran into several GFLOPS, an absolutely impressive level at that time.

Teams from Audio Ease, Sony and Yamaha flew around the world, sampling the most prestigious concert halls, churches and stages. Sampling Het Concertgebouw in Amsterdam, for example, required to hire the venue for one night – 7PM to 7AM, working with a team of engineers to record impulse responses in the large and small hall. Deeply into the night to avoid background noise from the Amsterdam trams.

Still today, the libraries of the three companies can be used. AltiVerb is still for sale as VST plug-in, along with a huge library of samples that is still maintained. The Yamaha SREV1 and Sony DRE-S777 are no longer produced, but the Yamaha samples are still used in several product lines: the AFC3 acoustic enhancement system, the series of RX-V Musiccast AV receivers, and in the Steinberg Reverence VST plug-in library for Nuendo and Cubase.

To indicate how much hardware processing has evolved since then, we tested how many occurrences of a 5.1 Reverence plug-in we could run on a Nuage system installed on a HP z840 GHz 8-core Xeon computer at a recent trade show – everything to kill a dull moment. At the 25th Reverence occurrence, the processor was still under 50%... we gave up. It’s literally possible to run dozens of convolution plug-ins on modern DAW’s and DSP engines such as the Waves SoundGrid server.

If you would like to go deeper into the topic of convolution reverberation, check out the further reading materials below, or go to one of our YCATS Yamaha Commercial Audio Seminars.
You can find the European schedule on www.yamahaproaudio.com/training

Next week’s micro tutorial will focus in on the damping factor of power amplifiers.