Reverberation frequency

Reverberation frequency a calculated feature derived from Count-Count to Peak divided by Duration-Rise time . 

It would normally be necessary to locate more than one monitoring unit on a structure. Thus each unit will only transmit its information on receiving coded instructions. Surface units can commonly accommodate up to 80 different codes. The ability to interrogate and receive over any distance is dependent upon the acoustic operation frequency. Relatively high frequencies are preferable, as they avoid problems of pulse reverberations and echoes from structural members. Typically data can be transferred over a distance of 2 km. This type of acoustic unit gives accuracies in potential measurement of 10mV. 

In the acoustic microscope the required signal can be selected not only in the time domain but also in the frequency domain. The ability to select the specimen echo and separate it in time from the unwanted lens echo was the basis of the design considerations of the focal length of the lens, and hence the resolution available ( 3.2 and 4.3). But it is a feet of experience that smaller lens reverberations are always present that cannot be separated in time from the echo from the specimen. These lead to the kind of problem that was illustrated schematically in Fig. 4.5. Moreover, even if such reverberations... 

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 ... 

Figure 3.27 Reverberator constructed by associating a frequency dependent absorptive filter with each delay of a lossless FDN prototype filter [Jot and Chaigne, 1991].

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

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. 

Reverberator constructed with frequency dependent absorptive filters 124... 

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. 

When the room is highly idealized, for instance if it is perfectly rectangular with rigid walls, the reverberant behavior of the room can be described mathematically in closed form. This is done by solving the acoustical wave equation for the boundary conditions imposed by the walls of the room. This approach yields a solution based on the natural resonant frequencies of the room, called normal modes. For the case of a rectangular room shown in figure 3.3, the resonant frequencies are given by [Beranek, 1986] ... 

Schroeder chose the parameters of his reverberator to have an echo density of 1000 echoes per second, and a frequency density of 0.15 peaks per Hz (one peak per 6.7 Hz). Strictly applying equation 3.27 using these densities would require 12 comb filters with a mean delay of 12 msec. However, this ignores the two series allpass filters, which will increase the echo density by approximately a factor of 10 [Schroeder, 1962], Thus, only 4 comb filters are required with a mean delay of 40 msec. 

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. 

Figure 3.21 Dattorro s plate reverberator based on an allpass feedback loop, intended for 29.8 kHz sampling rate [Dattorro, 1997]. //i(z)and H2(z) are low-pass filters described in figure 3.11 H (z) controls the bandwidth of signals entering the reverberator, and H2(z) controls the frequency dependent decay. Stereo outputs yL and yR are formed from taps taken from labelled delays as follows yL = a [266] + a[2974] - [1913] + c[1996] - < [1990] - e[187] - f[ 066], yR = < [353] + < [3627] - e[1228] + /[2673] - a[2111] - >[335] - c[121]. In practice, the input is also mixed with each output to achieve a desired reverberation level. The time varying functions u(t) and v(t) are low frequency (= 1 Hz) sinusoids that span 16 samples peak to peak. Typical coefficients values are gj = 0.75, g2 = 0.625, g3 = 0.7, g4= 0.5, g5= 0.9.

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