Splitting the unit delay [FIR/all pass filters design]

TLDR

A fractional delay filter performs bandlimited interpolation between samples and is used in communications, array processing, speech processing, music technology, modem synchronization, sampling‑rate conversion, pitch prediction, and musical‑instrument synthesis. The paper reviews FIR and all‑pass filter design techniques for bandlimited approximation of a fractional digital delay, emphasizing simple, efficient methods suitable for rapid coefficient updates or continuous delay control. The review examines design methods and evaluates their implementation complexity. The authors propose various new approaches and provide examples illustrating their performance.

Abstract

A 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. 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 filters are needed: synchronization of digital modems, incommensurate sampling rate conversion, high-resolution pitch prediction, and sound synthesis of musical instruments.