fractional delay filter is a device for bandlimited interpolation between samples. It finds applications in numerous fields of signal processing, including communications, array processing, speech processing, and music technology. In this article, we present a comprehensive review of FIR and allpass filter design techniques for bandlimited approximation of a fractional digital delay. Emphasis is on simple and efficient methods that are well suited for fast coefficient update or continuous control of the delay value. Various new approaches are proposed and several examples are provided to illustrate the performance of the methods. We also discuss the implementation complexity of the algorithms. We focus on four applications where fractional delay filers are needed: synchronization of digital modems, incommensurate sampling rate conversion, high-resolution pitch prediction, and sound synthesis of musical instruments. 30 IEEE SIGNAL PROCESSING MAGAZINE

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An inherent property of many DSP algorithms is that they tend to exhibit uniform frequency resolution from zero to Nyquist frequency. This is a direct consequence of using unit delays as building blocks; a frequency independent delay implies uniform frequency resolution. In audio applications, however, this is often an undesirable feature since the response properties are typically specified and measured on a logarithmic scale, following the behavior of the human auditory system. In this paper we present an overview of warped filters and DSP techniques which can be designed to better match the audio and auditory criteria. Audio applications, including modeling of auditory and musical phenomena, equalization techniques, aurahation, and audio coding, will be presented.

Computational modeling of musical instruments is an alternative to commonly used and more straightforward sound synthesis techniques like FM synthesis and waveform sampling. New powerful signal processors make it possible to run such models in real time. This paper deals with algorithms that can be used to synthesize guitar sounds on a floating-point signal processor. A FIR type Lagrange interpolator is introduced to implement efficient and precise fractional delay approximation that is needed to achieve arbitrary and varying length strings. This kind of interpolation is especially good in avoiding distortion and undesirable extra effects when the string length is changing continuously during the synthesis of a sound. The interpolator can also be used in other cases, e.g. in transmission-line modeling of acoustic tube resonators in wind instruments and also for vocal tract models in speech synthesis. In addition to the interpolation principle the paper describes the implementation of the guitar string model on the TMS320C30 floating-point signal processor.

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