Early reverberation

In this paper, we will concentrate on the perceptually motivated method, because the resulting recursive algorithms are more practical and useful. We first present a concise physical and perceptual background for our study of reverberation, then discuss algorithms to simulate early reverberation, and conclude with a discussion of late reverberation algorithms. 

The geometrical models allow the prediction of a room s early reverberant response, which will consist of a set of delayed and attenuated impulses. More accurate modeling of absorption and diffusion will tend to fill in the gaps with energy. Linear filters can be used to model absorption, and to a lesser extent diffusion, and allow reproduction of the directional properties of the early response. 

We are now prepared to discuss efficient algorithms that can render reverberation in real-time. For the case of early reverberation, the filter structures are fairly obvious. As we have already mentioned, convolution is a general technique that can be used to... 

The early reverberant response can be customized by injecting the input signal appropriately into the interior of the delay lines. 

When this giant breakthrough occurred, in the early 1950 s, its reverberations soon reached us at Akron, and this immediately prompted another invitation to Mark to "tell us all about it". He spoke to a packed house, again giving a lucid presentation not... 

The fact that the early and late reverberation have different physical and perceptual properties permits us to logically split the study of reverberation into early and late reverberation. 

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).

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. 

Figure 3.6 Combining early echoes and late reverberation [Schroeder, 1970b], B z) is a reverberator.

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. 

Figure 3.1 shows the impulse response of a concrete stairwell, plotting pressure as a function of time. The direct response is visible at the far left, followed by some early echoes, followed by the exponentially decaying late reverberation. The early echoes have greater amplitude than the direct response due to the directivities of the measurement speaker and microphone. 

Rooms may contain a large number of sources with different positions and directivity patterns, each producing an independent signal. The reverberation created in a concert hall by a symphony orchestra cannot be characterized by a single impulse response. Fortunately, the statistical properties of late reverberation do not change significantly as a function of position. Thus, a point to point impulse response does characterize the late reverberation of the room, although the early echo pattern is dependent on the positions and directivities of the source and receiver. 

Moorer proposed a slightly different structure, shown in figure 3.7, where the late reverb is driven by the output of the early echo FIR filter [Moorer, 1979], Moorer described this as a way of increasing the echo density of the late reverberation. The delays D and D2 can be adjusted so that the first pulse output from the late reverberator corresponds with the last pulse output from the FIR section. The gain g serves to balance the amount of late reverberation with respect to the early echoes. An important feature of this structure, apart from the early echo modeling, is the control... 

If the reverberation is not presented binaurally, the early lateral echoes will not produce spatial impression, but will cause tonal coloration of the sound. In this case it may be preferable to omit the early echoes altogether. This is an important consideration in professional recording, and is the reason why orchestras are often moved to the concert hall floor when recording, to avoid the early stage reflections [Griesinger, 1989],... 

The first artificial reverberators based on discrete-time signal processing were constructed by Schroeder in the early 1960 s [Schroeder, 1962], and most of the important ideas about reverberation algorithms can be traced to his original papers. Schroeder s original proposal was based on comb and allpass filters. The comb filter is shown in figure 3.12 and consists of a delay whose output is recirculated to the input. The z transform of the comb filter is given by ... 

Figures 5.15 and 5.16 show early time profiles for several of the cases studied. Note that higher hydrostatic pressure systems have nearly the same pressure-time profiles as do the lower hydrostatic pressure systems until the Tetryl-water interface pressure drops to near the hydrostatic pressure. The pressure gradient behind the water shock becomes less steep for the higher hydrostatic pressure systems and determines when the bubble will collapse. At lower hydrostatic pressures, many reverberations occur during expansion and collapse of the bubble. The pressure-time and pressure-distance profiles become very complicated.

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