Reverberation time

In addition to the distortions caused by the probes, there were also distortions caused by filtering the signals within the eddy-current test instruments. To achieve the highest possible dynamics with the test instruments, high-pass filters with a high rate of rise, but also a long reverberation time were used. Thus, the recorded C-scan pictures sometimes shows strong echo effects. 

Reverberation Control. Reverberation time (T q) is defined as the length of time in seconds for the sound of an instantaneously stopped source in a room to decay by 60 decibels (dB). Reverberation time is one important factor in determining the acoustical character of a space and its suitabiHty for specific activities. For lectures and other speech activities a relatively short reverberation time is desirable so that syllables do not persist and overlap one another, causing difficulty with inteUigibiHty conversely, for music activities, a relatively long reverberation time is desirable to allow blending of the sound and a sense of being surrounded by the music. Without reverberation music usually sounds dull and lifeless. 

The reverberation time in a room is direcdy proportional to the volume and inversely proportional to the amount of sound absorption in the room. For most practical purposes the reverberation time is determined by the Sabine equation ... 

Reverberation time The time required for a sound to fall to a given level in an enclosure. 

Typical pressure and temperature histories computed are shown in Figs. 6.6 and 6.7. In Figs. 6.6, the pressure is shown as a function of position within the powder compact at various times. For the baratol explosive loading shown, an initial wave, whose pressure is 1.8 GPa, is shown moving slowly from right to left. Upon reflection from the rear interface with the copper, the pressure jumps to a much higher value and then quickly reverberates to a peak pressure of about 11.4 GPa. The shorter reverberation time reflects the higher wavespeed and the major reduction in thickness in the compressed powder. 

Sabine s pioneering research started the field of modem room acoustics and established many important concepts, most notably the concept of reverberation time (RT) [Sabine, 1972], His initial experiments consisted of measuring the reverberant decay time of a room, and observing the change in decay time as absorptive material was added to the room. Sabine determined that the reverberant decay time was proportional to the volume of the room and inversely proportional to the amount of absorption ... 

Figure 3.4 Energy decay relief for occupied Boston Symphony Hall. The impulse response was measured at 25 kHz sampling rate using a balloon burst source on stage and a dummy-head microphone in the 14th row. The Schroeder integrals are shown in third octave bands with 40 msec time resolution. At higher frequencies there is a substantial early sound component, and the reverberation decays faster. The frequency response envelope at time 0 contains the non-uniform frequency response of the balloon burst and the dummy-head microphone. The late spectral shape is a consequence of integrating measurement noise. The SNR of this measurement is rather poor, particularly at low frequencies, but the reverberation time can be calculated accurately by linear regression over a portion of the decay which is exponential (linear in dB).

In the absence of any other information, the mid-frequency reverberation time is perhaps the best measure of the overall reverberant characteristics of a room. We expect a room with a long RT to sound more reverberant than a room with a short RT, However, this depends on the distance between the source and the listener, which affects the level of the direct sound relative to the level of the reverberation. The reverberant level varies little throughout the room, whereas the direct sound falls off inversely proportional to distance. Thus, the ratio of direct to reverberant level is an important perceptual cue for source distance [Blauert, 1983, Begault, 19921. 

The late reverberation is characterized by a dense collection of echoes traveling in all directions, in other words a diffuse sound field. The time decay of the diffuse reverberation can be broadly described in terms of the mid frequency reverberation time. A more accurate description considers the energy decay relief of the room. This yields the frequency response envelope and the reverberation decay time, both functions of frequency. The modal approach reveals that reverberation can be described statistically for sufficiently high frequencies. Thus, certain statistical properties of rooms, such as the mean spacing and height of frequency maxima, are independent of the shape of the room. 

Thus, in order to simulate a perceptually convincing room reverberation, it is necessary to simulate both the pattern of early echoes, with particular concern for lateral echoes, and the late energy decay relief. The latter can be parameterized as the frequency response envelope and the reverberation time, both of which are functions of frequency. The challenge is to design an artificial reverberator which has sufficient echo density in the time domain, sufficient density of maxima in the frequency domain, and a natural colorless timbre. 

Equation 3.24 specifies the minimum amount of total delay required. In practice, low modal density can lead to audible beating in response to narrowband signals. A narrowband signal may excite two neighboring modes which will beat at their difference frequency. To alleviate this, the mean spacing of modes can be chosen so that the average beat period is at least equal to the reverberation time [Stautner and Puckette, 1982], This leads to the following relationship ... 

Schroeder s original reverberator sounds quite good, particularly for short reverberation times and moderate reverberation levels. For longer reverberation times or higher levels, some sonic deficiencies become noticeable and these have been described by various authors [Moorer, 1979, Griesinger, 1989, Jot and Chaigne, 1991] ... 

For longer reverberation times, the reverberation sounds tonally colored, usually referred to as a metallic timbre. 

There are many possible reverberation algorithms that can be constructed by adding absorptive losses to allpass feedback loops, and these reverberators can sound very good. However, the design of these reverberators has to date been entirely empirical. There is no way to specify in advance a particular reverberation time function A(co), nor is there a deterministic method for choosing the filter parameters to eliminate tonal coloration. 

Once a lossless prototype has been chosen, the absorptive filters and the correction filter need to be implemented based on a desired reverberation time curve. Jot has specified a simple solution using first order HR filters for the absorptive filters, whose transfer functions are written [Jot, 1992b] ... 

The filter parameters are based on the reverberation time at zero frequency and the Nyquist frequency, notated T, (0) and 7 ,(7C), respectively ... 

The derivation of these parameters is detailed in the reference [Jot, 1992b]. The family of reverberation time curves obtained from first order filters is limited, but leads to natural sounding reverberation. Jot also describes methods for creating higher order absorption and correction filters by combining first order sections. 

Jot s method of incorporating absorptive filters into a lossless prototype yields a system whose poles lie on a curve specified by the reverberation time. An alternative method to obtain the same pole locus is to combine a bank of bandpass filters with a bank of comb filters, such that each comb filter processes a different frequency range. The feedback gain of each comb filter then determines the reverberation time for the corresponding frequency band. 

The performance of a head-mounted two-microphone adaptive noise-cancellation system was investigated by Weiss [Weiss, 1987] and Schwander and Levitt [Schwander and Levitt, 1987]. In this system, an omnidirectional microphone was used for the speech signal and a rear-facing hypercardioid microphone mounted directly above the speech microphone was used for the noise reference. In a room having a reverberation time of 0.4 sec, this system improved the speech recognition score to 74 percent from 34 percent correct for the unprocessed condition for normal-hearing listeners given... 

Assuming a direct path exists between the source and the listener, the listener will first hear the direct sound, followed by reflections of the sound off nearby surfaces, which are called early echoes. After a few hundred milliseconds, the number of reflected waves becomes very large, and the remainder of the reverberant decay is characterized by a dense collection of echoes traveling in all directions, whose intensity is relatively independent of location within the room. This is called late reverberation or diffuse reverberation, because there is equal energy propagating in all directions. In a perfectly diffuse soundfield, the energy lost due to surface absorption is proportional to the energy density of the soundfield, and thus diffuse reverberation decays exponentially with time. The time required for the reverberation level to decay to 60 dB below the initial level is defined as the reverberation time. 

The late portion of the EDR can be described in terms of the frequency response envelope G(a) and the reverberation time Tr (co), both functions of frequency [Jot, 1992b], G(co) is calculated by extrapolating the exponential decay backwards to time 0 to obtain a conceptual EDR(0, co) of the late reverberation. For diffuse reverberation, which decays exponentially, G(co) = EDR(0, co). In this case, the frequency response envelope G(co) specifies the power gain of the room, and the reverberation time Tr (CO) specifies the energy decay rate. The smoothing of these functions is determined by the frequency resolution of the time-frequency distribution used. 

Let us consider attempting to create a reverberator using a single comb or allpass filter. For the case of a comb filter, the reverberation time Tr is given by ... 

All reverberation algorithms are susceptible to one or more of these faults, which usually do not occur in real rooms, certainly not good sounding ones. In addition to these criticisms, there is the additional problem that Schroeder s original proposal does not provide a frequency dependent reverberation time. 

Despite these improvements many problems remained. The frequency dependent reverberation time is the net result of the lowpass filtering, but it is not possible to specify a function 7 ,(oi) which defines the reverberation time as a function of frequency. Furthermore, the recurring problems of metallic sounding decay and fluttery late response are reduced but not entirely eliminated by this reverberator. 

The resulting reverberator can be specified in terms of the desired reverberation time T r (GO) and frequency response envelope G(co). 

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