Reverberation based method

The reverb has room modes such as church, small club, living room or gymnasium. We can select the mode of Reverb filter to produce the effect of the true environment. The algorithm of reverb can make the sound have more surround effect. There are many important properties about the room response needed to be considerer in the design of efficient reverberators and we will discuss them as follow.

Echo Density

In the time domain, the echo density of a room response was defined as the number of echoes reaching the listener per second.

4 ( )3 differentiating with respect to t, we obtain that the density of echoes is proportional to the square of time: independent of the room shape and is given as follow:

3 2

2

Thus, the modal density of a room response grows proportionally to the square of the frequency.

Reverberation Time

The room effect is often characterized by its reverberation time, a concept first established by Sabine in 1990. The reverberation time is proportional to the volume of the room and inversely proportional to the amount of sound absorption of the walls, floor and ceiling of the room. The Sabine’s empirical formula estimating the reverberation time is used for estimating the degree of sound absorption in a room.

Energy Decay Curve (EDC) and Energy Decay Relief (EDR)

The method to determine the reverberation time of a measured room is finding the time when the associated sound pressure attenuate 60 dB in the plot of the EDC, Schoroeder proposed in 1965. He suggested integrating the impulse response of the room to get the room’s energy decay curve.

the EDC to help visualize the frequency dependent natural of reverberation called the energy decay relief EDR t( , )ω . The EDR represents the reverberation decay as a function of time and frequency in a 3D plot. To compute it, we divide the impulse response into multiple frequency band and compute Schoroeder;s integral for each band.

Modeling Early Reflection

A room response from a source to a listener can be obtained by solving the wave equation also known as the Helmholtz equation. However, it can seldom be compared to the area of surface in the room and large compared to the roughness of surface, all phenomena due to the wave nature, such as diffraction and interference, are ignored. The image-source method examines the effects of an acoustic source in a room with corresponding sources located in image rooms with reflecting boundaries.

Each of the infinite sources will produce attenuated, filtered and delayed version of number of points filter. One method to deal with the large size FIR filter is using an

algorithm based in the Fast Fourier Transform (FFT) block convolution [33]. The second method is try to model the late reverberation of a room based on some IIR-filters, comb and all-pass filters, Schoroeder proposed first in the early 1960’s, or a mixture of them. The details of comb filter and all-pass filter will be discussed in the next section.

Comb Filter

The block diagram of comb filter shown in Fig. 13 consists of a single delay line of m samples with a feedback loop containing an attenuation gaing. The z- transform of the comb filter is given by:

( ) 1 Note that to achieve stability, gmust be less than unity. The time response of this filter is an exponentially decaying sequence of impulse spaced m samples apart.

This is good for modeling reverberation because real room have a reverberation tail decaying somewhat exponentially. However, the echo density is really low, causing a “fluttering” sound on transient input. The pole-zero map of the comb filter shows that a delay line of m samples creates a total of m poles equally spaced inside the unit circle when it is stable. Half of the poles are located between 0 Hz and the Nyquist frequency f = f_s/ 2Hz, where f_sis the sampling frequency. That is why the frequency response has m distinct frequency peaks giving a “metallic” sound to the reverberation tail. We perceive this sound as being metallic due to hearing the few decaying tones that correspond to the peaks in the frequency response.

All-pass Filter

Because the poor performance of frequency response of a comb filter, Schroeder modified to provide a flat frequency response by mixing the input signal and the comb filter output as shown in Fig. 14. The resulting filter is called an allpass filter

because its frequency response has unit magnitude for all frequencies. The z-transform of the all-pass filter is given by:

( ) 1 all-pass filter now has zeros at the conjugate reciprocal locations.

And the response of an all-pass filter sounds quite similar to the comb filter, tending to create timbre coloration.

Nested All-pass Filter

To achieve a more natural-sounding reverberation network, it would be desirable to combine the unit filters to produce a buildup of echoes, as it would occur in real rooms. One solution to produce more echoes is cascading multiple all-pass filters which Schroeder had experimented with reverberators consisting of 5 all-pass filters in series. Schroeder noted that these reverberators were indistinguishable from real rooms in terms of coloration, which may be true with stationary input signals, but other authors have found that series all-pass filters are extremely susceptible to tonal coloration, especially with impulsive inputs. Gardner proposed reverberators based on a “nested” all-pass filter, where the delay of an all-pass filter is replaced by a series connection of a delay and another all-pass filter. The block diagram and its impulse response are shown in Fig. 15(a), where the all-pass delay is replaced with a system functionN z( ), which is all-pass. Then the transfer function of this from is written:

1 response in Fig. 15(b). Echoes created by the inner all-pass filter are recirculated to itself via the outer feedback path. Thus the echo density of a nested all-pass filter increases with time, as in real rooms.