HeadWize - Technical Paper: Convolution Processing for Realistic Reverberation by Andrew Reilly and David McGrath

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Convolution Processing for Realistic Reverberation by Andrew Reilly and David McGrath Abstract Arbitrary reverberation impulse responses may be applied to real time audio data by the use of long convolution. This paper outlines the techniques for measuring, generating and manipulating reverberation functions. In addition, some less traditional functions are proposed as reverberation impulse responses for use as musical effects. 1. Introduction One area of audio technology that has seen substantial benefits from DSP technology in the recent past is reverberation processing. Unlike other areas in audio, where DSP methods are often used to simply mimic the equivalent analog circuit, reverberation systems implemented with DSP are popular because they are capable of creating effects that were not previously achievable with analog circuits. The main differences between traditional DSP reverberation techniques and the new methods proposed in this paper are illustrated in Figure 1. The traditional methods rely on carefully designed DSP structures built from delays, feedback paths and gain blocks. In addition, careful manipulation of delay and gain parameters is required to map the parameters selected by the user (decay time, room size, room shape etc...). Hence, the quality of the reverberation is determined by both the DSP code and the methods used by the controlling process to map user settings to DSP delay/gain parameters. In contrast, the new methods proposed in this paper do not rely on any specific qualities in the DSP code being tailored towards reverberation. This new technique for reverberation processing breaks the system into two components. The first part of the reverberation system is an FIR filter long enough to implement impulse responses in excess of 4 seconds. A pair of these filters is required to produce stereo output. The second important part of the reverberation system is the FIR filter coefficient generation method. This involves software (possibly non-real time) running on the DSP or on a separate host processor. This paper is divided into nine sections. Part 2 of the paper explains the way that real room reverberation can be mimicked by long FIR filters. Part 3 examines the new methods used for artificial reverberation and computer room modelling systems that simulate room reverberation. Part 4 looks at some simple methods that may be used to modify pre-computed or measured room responses to achieve some control over the reverberation characteristics of the system. Part 5 includes a brief description of the FIR filters implemented on the Lake Huron Digital Audio Convolution Workstation. Part 6 introduces a new concept for reverberation/effects processing by using sampled sounds as convolution coefficients. 2. Implementing reverberation responses as FIR coefficients Apart from ad-hoc work-arounds to address deficiencies in some simplified DSP techniques, a reverberator can be classified as a linear time invariant system. This implies that the system can be described by its impulse response. (Some reverberation systems do contain time varying components, to provide more randomisation of the tail of the reverberator, thus disguising unwanted colouration that might be introduced by the reverberation algorithms used.) If we consider the impulse response of the reverberator to be finite in duration (and for most systems this will be true if we ignore inaudible information at the end of the tail of the response) then we can implement the desired reverberation function using a Finite Impulse Response (FIR) filter. The behaviour of linear time invariant systems is well understood, and systems with finite impulse response can be measured and simulated in a straightforward manner. As an example of the way we can measure the impulse response of a complex system, consider a sound system in a reverberant acoustic space. We define the system as consisting of the following components: A power amplifier that takes the system input and applies it to a loudspeaker. The loudspeaker, placed in a particular location within the room, with a particular frequency response and directivity pattern. The room itself, with floor, ceiling and walls with particular reflection properties. The receiver, such as a microphone, placed in a particular location, with a particular frequency response and directivity pattern. If we consider this entire configuration of components to be one linear system, then we can apply a stimulus at the input terminals of the amplifier and measure the response at the output lead of the microphone. In the particular case where the stimulus is an impulse, the response measured is referred to as the impulse response. The impulse response will typically appear as shown in Figure 2. Figure 2 The impulse response of a linear system is important because it can be used directly by an FIR filter to implement an equivalent system. For example, the impulse response shown in Figure 2 can be loaded as filter coefficients into an FIR filter, and that filter will then mimic the entire electro-acoustic system, including the amplifier, speaker, room and microphone. Because the electro-acoustic system that we measured included a reverberant acoustic space, this FIR filter is performing the function of a reverberator, taking dry input audio and making it more reverberant. All of the qualities of brightness, diffusion, reverberation decay time etcetera of the original system will be preserved in the FIR implementation. By measuring real acoustic spaces, we are then able to optimise our reverberation responses by the following means: We can select rooms that are already well known for their desirable acoustic properties. We can arrange the sound source in an appropriate position in the room to achieve the best acoustic result. We can arrange the microphone(s) appropriately to achieve the best possible recording. The choice of microphone arrangement for room measurement can be made in exactly the same way that we would arrange the microphones for making recordings in the same room. If we choose a specific stereo microphone technique for making our measurement, or even if we use a dummy head to make a binaural measurement, then the room response that we measure will contain all of the characteristics of that microphone technique. Figure 3 shows the relationship between the measurement technique and the playback method. The result achieved when the dry vocal audio is processed through the pair of FIR filters is identical to the result that we would expect if the same vocalist was recorded in the real acoustic space, with the following exceptions: The directivity pattern of the vocalist may not match the directivity pattern of the source (loudspeaker) used in the room measurement. The vocalist will be singing in a booth, not on a real stage, and will thus be lacking some of the cues that exist in on the real stage. These cues could include acoustic feedback to the vocalist and the effect of the audience on the mental state of the vocalist. 3. Simulated architectural acoustics As an alternative to measuring real acoustic spaces, new methods for simulation of acoustic spaces are now making it possible to create acoustic impulse responses based on a computer model of the space. These techniques have the advantage that the acoustic space under analysis does not have to exist in reality. The acoustic simulation programs available today are generally tailored towards the goal of allowing an acoustics practitioner to analyse the characteristics of a new or modified space prior to the expensive construction or renovation of the space. These programs produce a large amount of numerical and graphical data that can provide the user with insights into parameters of the room such as reverberation decay time, ratio of direct to reflected energy, and speech intelligibility. As with the case of a measured room, this acoustic analysis is based on a specific source location and directivity as well as the listener/microphone location, directivity and configuration. Based on the selection of source and microphone locations etcetera, more recent acoustic simulation systems are now capable of producing an impulse response (or stereo pair of impulse responses) describing the response at the microphone (or dummy head) based on an impulse transmitted at the source. The goal of acoustic simulation systems is to make these impulse responses sufficiently accurate to allow the user to make subjective judgements regarding the acoustic qualities of the space. The technique of listening to computer simulated impulse responses, processed through FIR filters, is known as Auralization[1]. Auralization is available today with a number of simulation packages, including the Bose Auditioner system[2], CATT Acoustic room simulation[3], and the ADA EASE system[4]. Initially, a goal of the research into auralization was to simply present the user with an acoustic experience that conveyed some important aspects of the room acoustics. The auralization did not necessarily have to sound exactly like the real room, provided the listener was well trained and understood what differences might be expected to exist between the simulation and the real room. In this case, the impulse response generated by the simulation software may not be considered as 'high-quality' in the context of reverberation processing. However, as auralization technology improved, simulation software (including the four systems mentioned above) has been refined to make the room impulse responses more accurate, to the point where most listeners could not distinguish between measured and synthetic impulse responses, when they are used in FIR filters to process reverberation. These developments in acoustic simulation are now yielding a new capability for artificial reverberation to be created based on accurate room parameters, with the reverberation responses being entirely computer generated. For example a reverberator can be implemented based on a user's input, specifying the size and shape of a room, the placement of speakers, the placement of the microphone/dummy head, and the acoustic properties of the wall, floor and ceiling materials. Potentially, this method for implementing reverberation offers all of the benefits of the room-measurement methods, with the added convenience of being able to select and adjust room parameters very quickly. 4. Manipulating reverberation responses Any subjective judgements that can be made about the aesthetics of an acoustic space are generally based on some notional ideal acoustic space. The ideal space that is referenced for comparisons will differ depending on the anticipated application that the space is intended for. Concert halls, jazz clubs, business offices, chamber music venues all have different ideal impulse responses. This raises the question : If an acoustic space is generally considered to be less than ideal in its acoustic properties, is it possible to take the measured impulse response of this hall and manipulate it in a way that improves its response? Many of the common problems that can occur with acoustic spaces include: Resonances, particularly in small acoustic spaces. These can be isolated in the tail of a measured impulse response and filtered out. Reverberation time too long or too short. The reverberation time of the room may be longer or shorter than required. The reverberation time can be measured in each octave band, and problems with the reverberation time can be corrected in the measured impulse response by multiplying the impulse response (or just some selected octave bands of the impulse response) by a decaying or growing exponential function. Large localised echoes in the early part of the response. These can be located and removed from the measured impulse response. Note that the methods used to fix these acoustic 'problems' do not require any fixes to the geometry or acoustic properties of the hall. Rather, the correction is done only to the measured response, effectively removing the symptom rather than the cause. Another method that could be used, in the case of acoustic simulation software, would be to allow the user to examine the acoustic properties of the space and then modify these acoustic properties in some way before the simulation software computes its impulse response. For example, if the acoustic simulation software is capable of predicting resonances, reverberation times or the occurrence of localised echoes, then it is possible that the software could then be capable of removing these artefacts during the process of computing the impulse response. Taking this a step further, it would also be possible to remove any direct computation on room geometry from the simulation software, and allow impulse responses to be created based solely on the user's requested parameters of room size, room shape, reverberation decay time etcetera. In this case, the software that generates the impulse response is less suitable for scientific purposes and more suited to reverberation as an artistic tool in audio. Many of the important lessons that have come out of the research into auralization will enable these computer generated reverberation responses to be more like real rooms, and more natural in their sound compared to the response of the current reverberation processors that use delay-lines and feedback. 5. The FIR filter implementation The interest in applying long FIR processing to reverberation has been spurred on recently by the advancing capability of modern DSP systems. Lake DSP has built a variety of different systems for performing long FIR processing. Early systems built by Lake were based on fast convolution, a method that makes use of Fast Fourier Transforms (FFTs) to speed up the very compute intensive task of convolution. Traditional fast convolution techniques operate on data in blocks, which causes considerable delays through the processing. More recently, Lake has produced a DSP system known as Huron which is capable of implementing long convolution without delay. FIR filters with up to 262144 taps can be implemented on the Huron system, making it possible to simulate rooms with reverberation times greater than 5 seconds (running at a 48kHz sample rate). These filters can now be used in real-time live audio applications. 6. Sampled reverberation effects A new area of research at Lake is the use of sampled audio clips as FIR filter responses. This technique allows any piece of audio (usually fairly short in duration) to be loaded into the FIR filters and used as the FIR coefficients. As an example, a single short spoken word can be sampled and loaded into the FIR filter. When this filter is provided with an impulsive sound at its input, the output of the filter will be the original spoken word. Musical instruments with impulsive characteristics (such as piano, guitar, drums) can be processed with a vocoder-type effect by applying this technique. 7. Future work Further work occurring now and planned for the near future at Lake includes the following: Research into new ways to animate reverberant FIR responses more smoothly and rapidly. This involves using DSP processors to rapidly compute impulse responses.* Research into techniques for multi-channel reverberation for larger sound systems, such as cinemas. Research into virtual reality acoustic systems that allow simulation of multiple interconnected acoustic spaces with multiple animated sources and a roving listener. This research is already yielding some favourable results. 8. Conclusion A method has been described for implementing reverberation by using FIR filters, thus allowing all of the aesthetic requirements for the reverberation responses to be handled in a non real time manner. Four methods for creating reverberation responses were presented, (1) measurement of existing spaces, (2) computer simulation of existing or virtual spaces, (3) modified real or simulated responses, and (4) the use on alternative audio signals as reverberation responses. 9. References M. Kleiner, "Auralization: a DSP approach", Sound and Video Contractor, Sept 20, 1992. Bose Corporation, 100 Mountain Rd, Framingham MA 01701, USA CATT, Mariagatan 16A, S-414 71 Gothenburg, Sweden Acoustic Design Ahnert, Gustav-Meyer-Allee 25, D-13355 Berlin c. 1995, Lake DSP. From Lake DSP Pty.. (Republished with permission.) Questions or comments? Visit the HeadWize Discussion Forums.

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