Roomacousticsmeasurentsdoc Angelo Farina.doc

iacma international advanced course on musical acoustics bologna, italy, july 18-22, 2005 1 room acoustics measurements and auralization lamberto tronchin (1), angelo farina (2) (1) dienca - ciarm, university of bologna viale risorgimento, 2 - 40136 bologna, italy email: lamberto.tronchinunibo.it url: www.ciarm.ing.unibo.it (2) industrial engineering dept., university of parma via delle scienze 181/a, 43100 parma, italy email: angelo.farinaunipr.it url: www.angelofarina.it abstract this document is divided in two parts: objective assessment of the acoustical quality of a room based on measurements, and perceptual assessment of the musical listening experience in a room based on the auralization technique. the basic quantity measured inside a room is its impulse response. therefore, the concept of impulse response is explained, and its limits clearly stated. then it is shown what are the best techniques for measuring impulse responses in typical rooms employed for musical performances, and how the concept of impulse response can also be applied for evaluating recording and reproduction rooms and equipment employed for the electro acoustical delivery of live or recorded music. similarly, the electro acoustical devices employed in room acoustic measurements (sound sources, microphones, digital playback/recording equipment, software) are surveyed. finally, the usage of measured (or computer-simulated) impulse responses for performing listening test through the auralization technique is presented, in its various technical embodiments. the realization of a virtual listening room is presented, and the pros and cons of each recording/reproduction approach are comparatively evaluated. 2 1 introduction to digital sound processing both when employing advanced measurement techniques or performing listening tests employing modern digital recording/reproduction equipment it is important to have a solid and simple grasp of the basic technology which makes it possible to process digitally the sound signal. although this knowledge is nowadays widespread, and people is used to digital sound and music since the childhood, thanks to technologies such as cd players, gsm cellular phones and mp3 music players, it is advisable to present here a very quick and basic explanation of the processing. this chapter has also the goal to explain the internal working of some devices which will be later employed during measurements and auralization, such as microphones, analog-to-digital converters, etc. the digital signal processing section contain very basic, but up-to-date information about manipulation of digital audio on modern platforms. 1.1 nature of the sound field the sound is a complex thermofluidodynamic phenomenon occurring in fluids and solids, which involves motion of the “particles” around their steady position (and hence the concept of “particle velocity”) and fluctuation of the density and pressure of the medium (and hence the concept of “acoustical pressure”, which is the difference between the absolute pressure and the long-term average pressure of the unperturbed medium). usually the human body is submerged in air, and the sound is perceived by the human being as an air-transmitted stimulus. various parts of the human body are sensitive to the acoustic field, (ears, skin, chest, stomach, etc.), and the human sensory system can detect both the particle velocity and the acoustical pressure. it must be noted that the acoustical pressure is a scalar quantity, and does not involve any directional information, whilst the particle velocity is a vector, and carries the information of the direction of propagation of the sound. although in very simple cases there exist analytical formulas relating particle velocity and acoustical pressure, in most real-world cases none of such simple relationships hold. most acoustics textbooks only explore satisfactorily these very simple cases, and leave the impression that complex, real-world cases can be explained as superposition of these basic cases. although this is in general true for the acoustical pressure field, this is not the case for the particle velocity field, and, more importantly, for the relationship between acoustical pressure and particle velocity. this relationship can be expressed in two ways: othe product between acoustical pressure p and particle velocity v is the sound intensity i: (1) vpi othe ratio between acoustical pressure p and particle velocity v is the impedance z: (2) v/pz 3 abandoning the usual limitations encountered in acoustics textbooks (steady- state periodic signals, etc.), both the instantaneous intensity signal i() and the impedance ratio z() are variables, and only in very particular cases these quantities have constant values and simple mathematical expressions. on most textbooks, the time average of the instantaneous intensity, named i, is considered constant, and similarly also the average value of the impedance ratio, named z, is considered constant. for proper handling of real-world cases, none of the above assumptions will be required here. instead, we can consider that, in general, acoustical pressure and particle velocity signals are completely unrelated, independent physical quantities, and that faithful recording and reproduction require capturing and recreating independently both of them. 1.2 from signals to numbers the conversion form the physical quantities known as sound pressure and particle velocity to a completely-numerical description of them is obtained by a chain of subsequent devices. 1.2.1 microphones the first stage is the existence of physical “transducers”: a microphone is a transducer transforming the acoustical quantity in electrical signals. as we already noted, in air the physical quantities are generally two (sound pressure and particle velocity), whilst the electrical signals can be voltage (volts), current (amperes) or charge (coulombs). regarding the first fact, we have basically “pressure microphones”, which do transduce the acoustical pressure in a corresponding proportional electrical quantity, and “velocity microphones”, which similarly transduce the “particle velocity” (or, more precisely, the cartesian component of the particle velocity along a well-defined axis) into a corresponding proportional electrical signal. some microphones, however, are “hybrid”, as they react both to acoustical pressure and to particle velocity, with a various “mix” of sensitivity to these physical quantities. this translates usually in a different directivity pattern of the mike, as shown in the following table: 4 namedirectivity sound pressure sensitivity particle velocity sensitivity omnidirectional100 %0 % subcardioid 0 330 300 270 240 210 180 150 120 90 60 30 75 %25 % cardioid 0 330 300 270 240 210 180 150 120 90 60 30 50 %50 % hypercardioid 0 330 300 270 240 210 180 150 120 90 60 30 25 %75 % figure-of-eight 0 330 300 270 240 210 180 150 120 90 60 30 0 %100 % some microphones are actually built employing a dual-diaphragm assembly: this makes it possible to vary the “mix” of pressure and velocity sensitivity acting on an electrical control device, usually a knob or a rotary dial, which enables the user to vary the directivity pattern of the microphone. the following figure shows one of these variable-directivity microphones, manufactured by neumann, whilst similar devices are built also from competitors such as schoeps, sennheiser, etc. 5 figure 1 neumann u89i variable-pattern microphone the electrical signal (voltage, current or charge) is always conditioned and converted in true-voltage by means of electronic circuitry, nowadays usually embedded inside the microphone body. so, in practice, from the microphone body the electrical signal is always output in form of a voltage signal, and consequently the absolute sensitivity of the mike can be expressed in mv/pa (millivolts per pascal), in the case of a purely-pressure microphone, or mv/ms-1 (millivolt per meter/second) in the case of a purely-velocity microphone. but in practice, as most people is trained not to think in terms of particle velocity, also for velocity microphones (or hybrid ones) the sensitivity is usually improperly expressed as mv/pa, assuming the special case of a plane, progressive waves (one of those special, simple cases always employed in textbooks), for which the ratio between acoustical pressure and particle velocity z is constant, and equal to c, which in air is usually equal to approximately 400 rayl (the unit of impedance, kg/m2s). so, for example, the sensitivity of the neumann u89i is declared as 8.0 mv/pa, even when the unit is operated as a pure figure-of-eight mike, in which case the “real” sensitivity should be expressed as 3200 mv/ms-1. 1.2.2 cables now we have a voltage signal, which can be manipulated in various ways. the signal can be amplified, so that the signal amplitude of a few millivolts is boosted to several volts, making it possible to transmit it over long cables. however, it is not common to see a significant voltage boost directly at the microphone assembly. instead, some sort of cabling always interconnects the mike with the preamplifier. a trick often employed for transmitting a weak signal over long cables without too much noise contamination is to use a “balanced” connection, which means employing a double signal cable surrounded by a ground screen. the signal is sent on both of the internal cables, but in one of them it is “positive” or “hot” (a pressure above the average air pressure is transferred into a positive-voltage electrical signal), whilst on the other wire it is polarity-reversed, also called “negative” or “cold”. at the end of the cable, the preamplifier or the recording device will extract a 6 signal which is given by the difference between the voltage detected across the pair of wires, and this simple fact rejects any contaminating noise which could have been entered the long cable. figure 2 balanced audio cables with xlr connectors (3 pins) most professional microphones and preamplifiers/recording devices are equipped with balanced connections, whilst low-end consumer, or high-end audiophile systems are usually “unbalanced”, and hence very sensitive to the quality of cabling. for consumer systems this choice is done for reducing the cost (as truly balanced input stages can cost 10 to 20 usd per channel, which is considered too expensive for a cheap consumer device), whilst for audiophile devices (which, costing thousands of dollars, should not have any problems accommodating the cost of high quality balanced input stages) the choice of unbalanced connections is made just for making room for “audiophile cables”, which again cost thousands of dollar, and would be absolutely useless if balanced connections were employed for interconnecting all the equipment. 1.2.3 preamplifier we are now at the fourth stage of the recording chain: after whats happing in the air, after the microphone, and after the cable, we usually find a preamplifier. in theory, the unique goal of a preamplifier is to boost the voltage generated by the microphone, bringing it at a level which is appropriate for the following equipment. in practice, however, very often the preamplifier also contain additional processing, which can either be linear (such as frequency-band limitation obtained by high-pass and low-pass filtering sections, often with switchable frequency limits) or notlinear, such as compression, soft-limiting, automatic gain control, squelch, etc. the presence of band-limiting function is inherently required by the electrical connection of microphones which require “phantom” power supply, obtained by means of a dc offset of both the “hot” and “cold” wires referred to the ground. this dc offset is typically set to 48 v for most microphones, and is employed for powering the electronics embedded inside the microphone body. the dc component needs to be decoupled from the audio signal, and usually a condenser is employed for this purpose, resulting in a gentle high-pass filter with a -3 db cutoff typically around 4 to 10 hz. this is of course of no concern for signals to be listened by humans, which are substantially deaf to sound having frequency below 16 hz. regarding the high frequency limit, modern equipment is usually configured 7 for very high frequency response, well in excess of 40 khz, even if there is no proof that humans can ear anything above 20 khz. it is thought, however, that the capability to handle very high frequencies causes the system to be more “transparent” to sharp attacks or pulsive sounds. the reality, instead, is that the capability to follow such sharp transients is not given by the extension of the pass-band, but by the temporal response of the low-pass filter: the smoother and softer is the frequency response of the filter, the shorter will be its response in time domain, and consequently the system will react promptly and without unwanted “ringing” in time domain. this is typically obtained with a soft low-pass, starting to roll off just above 20 khz (typically around 24 khz), but with a gentle slope, falling at -100 db only above 40 khz. the optimal shape of such a lowpass filter has been studied theoretically in 1, and is called an “apodising” filter. figure 3 2-channels microphone preamplifier the presence of not-linear sections in a microphone preamplifier is usually dictated by the need to not worry too much about accurate regulation of the gain of the preamplifier, making sure that, even if an unexpected sound comes very loud, the electronics will not going in clipping, causing nasty artifacts to the sound. this is a serious reason for employing such not-linear processors; but they can also be the cause of very dangerous measurement errors when employing the audio recording chain for room acoustics measurements. it is therefore recommended that, when the preamplifier is employed for measurements (opposed to recording live music), any notlinear section of the preamplifier is systematically excluded. in the following chapters it will discussed in great detail the kind of artifacts which arise when any part of the measurement chain exhibit notlinear behaviour. 1.2.4 adc (analog to digital converter) and finally, the signal can be converted from “analog” to “digital”, by means of a specific device (or a chip embedded in the preamplifier) called adc (analog-to- digital converter). the adc is a “black box” conceptually connected through just two wires. one wire is the input, bringing in the analog voltage signal, with a maximum allowed range of some volts (positive and negative). the second wire is the output, carrying out the digital information as a serial digital interface (bit after bit). the adc operation can internally be quite complex, but looking at it from outside we see basically just two types of converters, differentiated by the format of the output digital signal: pcm converters (pulse code modulation) and bitstream 8 converters (also called dsd, direct stram digital, or simply single-bit). the two techniques have some point in common (and, internally, either type of converters can make use of the same components and processing): the two relevant quantities of a multibit (pcm) converter are the sampling rate and the bit depth, whilst for a bitsream converter the number of bits is fixed to 1, whilst the sampling frequency can vary, being systematically much higher than the one employed in pcm comverters. lets start from the pcm converters, which are by far the more widely employed. a master clock defines with high precision the instants at which the analog signal has to be “sampled”. the operation of a pcm converter is bounded by the shannon theorem, which forces to use a sampling frequency which is at east double of the highest frequency contained in the analog signal. for audio applications, typical sampling frequencies are 44100 hz (cd), 48000 hz (dat, dvd-video) and 96000 hz (dvd-audio, hd recorders). even 192000 hz can be used in dvd-video (for 2 channels only) and on some soundcards employed on modern computers. as already explained, the goal of having sampling frequencies much higher than 40 khz is generally not to allow for an extended pass-band, but to allow for low- pass filters with a more gentle rolloff, ensuring crisp response to transients. however, another possible approach is to record with extended frequency pass-band, and later apply the “apodising” filters directly in the digital domain. in any case, it is very important that substantial low-pass filtering is applied in the analog domain, before entering the adc chip. in fact, if we feed the converter with signal having a content exceeding its limiting frequency (called nyquist frequency, and equal to half the sampling rate), the numerical representation of the signal is distorted, due to a phenomen known as “aliasing”, which reflect back to the sub-nyquist frequency band any signal having a frequency above it. if, for example, we feed without proper low-pass filtering a signal containing a pure tone (coming, for example, from a crt monitor) at 35 khz in a system working with a sampling frequency of 48 khz (hence with a nyquist frequency of 24 khz), we will get this tone “aliased” down to 13 khz (it was 11 khz above nyquist, so we find it 11 khz below it). one technique often used for reducing the aliasing problems is oversampling. instead of operating the converter at its nominal sampling frequency, we operate it at doubled frequency. this way, the chance that very high frequency content contaminates the conversion process is reduced. after the conversion is done, the data flow is “decimated” (if the sampling frequency was doubled, a sample each of two is discarded), of course after applying a proper low-pass filter (aliasing can occur also when decimating in digital domain, but designing suitable digital low pass fil