There are typically four steps in producing a CD or movie soundtrack, as shown in Figure 1. In tracking sounds are recorded or synthesized and arranged in tracks. The tracks are then processed in the mixing stage to form a stereo or multichannel mix. The idea is to arrange the sounds spatially and spectrally, to manipulate their character for artistic purposes, and also to fix problems in the tracks. In mastering, subtle adjustments and fixes are made to the mix, and often its dynamic range is limited in preparation for encoding and printing on the target medium.

An artificial reverberator having low memory requirements and small computational cost is presented. The reverberator consists of an equalized comb filter driving a convolution with a short noise sequence, which can consist of Gaussian or velvet noise. The reverberator equalization and decay rate are controlled by low-order IIR filters, and the echo density is that of the noise sequence. While this structure is efficient and readily generates high echo densities, if a fixed noise sequence is used, the reverberator has an unwanted periodicity at the comb filter delay length. To overcome this difficulty, the noise sequence is regularly updated or switched. Several structures for updating the noise sequence, including a leaky integrator sensitive to the signal crest factor, and a multiband architecture, are described.

Hybrid reverberators combine convolutional and feedback delay network (FDN) reverberators to exactly reproduce the psycoacoustically important reverberation impulse response onset while efficiently generating the needed late-field characteristics. A simple method for crossfading between the convolutional and FDN components of a hybrid reverberation is presented. It involves forming the convolutional impulse response as the windowed difference between the desired and FDN impulse responses. In this way, arbitrary windows may be applied to the convolution and FDN components of the hybrid reverberator impulse response in forming the crossfade. For applications in which the impulse response onset depends on a parameter, a singular value decomposition is used to develop a low-rank approximation to the tabulated reverberation impulse response onsets. The approximation is the combination of a few fixed impulse responses, with parameter-dependent weights. An emulation of the EMT 140 plate reverberator is presented as a sample application.

Pitch glide is an important effect that occurs in nearly all plucked string instruments. In essence, large amplitude waves traveling on a string during the note onset increases the string tension above its nominal value, and therefore cause the pitch to temporarily increase. Measurements are presented showing an exponential relaxation of all the partial frequencies to their nominal values with a time-constant related to the decay rate of transverse waves propagating on the string. This exponential pitch trajectory is supported by a simple physical model in which the increased tension is somewhat counterbalanced by the increased length of the string. Finally, a method for synthesizing the plucked string via a novel hybrid digital waveguide-modal synthesis model is presented with implementation details for time-varying resonators.

Pitch glide is an important effect that occurs in nearly all plucked string instruments. In essence, large amplitude waves traveling on a string during the note onset increases the string tension above its nominal value, and therefore cause the pitch to temporarily in- crease. Measurements are presented showing an exponential re- laxation of all the partial frequencies to their nominal values with a time-constant related to the decay rate of transverse waves prop- agating on the string. This exponential pitch trajectory is sup- ported by a simple physical model in which the increased tension is somewhat counterbalanced by the increased length of the string. Finally, a method for synthesizing the plucked string via a novel hybrid digital waveguide-modal synthesis model is presented with implementation details for time-varying resonators.

A method for designing audio lter s is developed based on the observation that second-order peaking and shelving lters can be made nearly self-similar on a log magnitude scale with respect to peak and shelf gain changes. By cascading such second-order sections, lter s are formed which may be t to dB magnitude characteristics via linear least-squares techniques. A graphic equalizer interpolating prescribed band gains is presented, along with a lter minimizing the Barkweighted mean square dB difference between modeled and desired transfer function magnitudes. It is noted that using second-order sections parameterized by transition frequency and gain provides a natural mechanism for slewing and interpolation between tabulated designs.

In some cases the reflection functions associated with the discontinuities in conical bores are growing exponentials [J. Martinez and J. Agul- ló, J. Acoust. Soc. Am. 84, 1613–1619 (1988)]. It is shown that discontinuities can be modeled by a Sturm–Liouville system using a pressurelike quantity as the dependent variable. For the subset of discontinuities exhibiting the growing exponential reflection function, the Sturm–Liouville potential function is an energy well. This well is shown to support exactly one trapped energy mode which corresponds to the growing exponential. It is shown that in the region surrounding the discontinuity for these systems, traveling Fourier components taken together with their reflected waves do not constitute a complete set and that the trapped mode is required to complete the set. On the other hand, for systems which do not exhibit the growing exponential, the Sturm–Liouville potential is an energy barrier with no trapped modes, and the Fourier components compose a complete set within the conical regions. Furthermore, a change of dependent variable can be used to go from a Sturm–Liouville description involving an energy well to one involving a barrier, thus eliminating the trapped mode.