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

  title={Splitting the unit delay [FIR/all pass filters design]},
  author={Timo I. Laakso and Vesa V{\"a}lim{\"a}ki and Matti Karjalainen and Unto K. Laine},
  journal={IEEE Signal Process. Mag.},
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… 

Optimal design of fractional delay filters

  • M. NagaharaY. Yamamoto
  • Computer Science
    42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)
  • 2003
It is shown that the optimal design problem is reducible to a norm-equivalent discrete-time problem and the modern sampled-data H/sup /spl infin// control which aims at restoring the intersample behavior is applied.

Principles of fractional delay filters

  • V. VälimäkiT. Laakso
  • Computer Science
    2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100)
  • 2000
An overview of design techniques and applications for digital fractional delay filters and their applications is given.

High-speed tunable fractional-delay allpass filter structure

A modified Thiran-based FD allpass filter structure is proposed that requires shorter critical path, less hardware complexity and improved frequency characteristics.

H-Inf-Optimal Fractional Delay Filters with Application to Pitch Shifting

A new approach based on the modern sampled-data H∞ optimization which aims at restoring the intersample behavior beyond the Nyquist frequency is proposed, and a closed-form solution is obtained under an assumption on the original analog signals.

Optimal design of fractional delay FIR filters without band-limiting assumption

  • M. NagaharaY. Yamamoto
  • Computer Science
    Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.
  • 2005
It is shown that the optimal FIR filter design is reducible to a convex optimization described by a linear matrix inequality (LMI) and a design example is shown to illustrate the advantage of the proposed method.

Variable cutoff frequency FIR filters: a survey

This paper presents a comprehensive review of the existing variable cutoff frequency FIR filter design techniques, including the developments in the recent two decades and the significant developments/incremental works thereof.


An algorithm for artistic spectral audio processing and synthesis using allpass filters is presented. These filters express group delay trajectories, allowing fine control of their

Variable fractional delay filters in bandlimited oscillator algorithms for music synthesis

Trivially sampled geometric waveforms such as the rectangular pulse wave used in subtractive sound synthesis suffer from aliasing caused by the discontinuities in the waveform or its derivative.

Maximally flat FIR and IIR fractional delay filters with expanded bandwidth

This paper discusses an alternative analytic formulation for FIR-FD filters, which in one special case coincides with the widely known so-called maximally flat FIR FD filters, and a way is found to apply this kind of optimization to IIR Allpass FD filters.

Digital interpolation in the passband domain

Techniques for digital interpolation in the passband domain are presented, exemplarily for a carrierless amplitude modulation/phase modulation (CAP) transmission system, and real-valued and complex-valued interpolation filters are shown to suffer from increasing center frequencies.



A novel implementation for narrow-band FIR digital filters

In an earlier paper Crochiere and Rabiner [1] discuss the theory of using finite impulse response (FIR) digital filters for signal decimation, interpolation, and filtering. In this paper we expand on

A continuously variable digital delay element

  • C. Farrow
  • Engineering
    1988., IEEE International Symposium on Circuits and Systems
  • 1988
An FIR (finite-impulse-response) filter which synthesizes a controllable delay which has the ability to interpolate between samples in the data stream of a band-limited signal is described.

Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial

Several applications of the polyphase concept are described, including subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion, digital crossover networks, and multirate coding of narrowband filter coefficients.

DSP implementation of arbitrary sampling frequency conversion for high quality sound application

A revision of the Ramstad hybrid structure which uses the B-spline function as analog resampler is presented and it is demonstrated that the B -spline functions give higher performances together with a reduced computational complexity.

Evaluation of several variable FIR fractional-sample delay filters

Four main FIR filter types are examined for applicability to the task of fractional-sample delay filtering, and the popular sinc delayer is shown to be a particularly poor performer.

A 2-channel, 16-bit digital sampling frequency converter for professional digital audio

A digital sampling frequency converter for arbitrary ratios of sampling frequencies is presented. It is based on a multistage interpolating filter, and on a novel time-domain control of the filter

Implementation of fractional delay waveguide models using allpass filters

The proposed structure can be applied to discrete-time modeling of acoustic tubes, such as the human vocal tract or resonators of musical instruments, using low-order allpass filters that are maximally-flat approximations of the ideal delay.

A digital signal processing approach to interpolation

In many digital signal precessing systems, e.g., vacoders, modulation systems, and digital waveform coding systems, it is necessary to alter the sampling rate of a digital signal Thus it is of

A new variable fractional sample delay filter with nonlinear interpolation

  • G.-S. LiuC. Wei
  • Engineering
    1991., IEEE International Sympoisum on Circuits and Systems
  • 1991
A finite impulse response (FIR) filter is presented which can synthesize any fractional sample delay by nonlinear interpolation by compensating for the delay time between the echo canceller output and the receiver input for the V.32 full-duplex modem or the U-transceiver in digital subscriber loop (DSL).

Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters

A new method of designing linear-phase FIR filters is proposed by minimizing a quadratic measure of the error in the passband and stopband. The method is based on the computation of an eigenvector of