# Principles of fractional delay filters

@article{Vlimki2000PrinciplesOF, title={Principles of fractional delay filters}, author={Vesa V{\"a}lim{\"a}ki and Timo I. Laakso}, journal={2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100)}, year={2000}, volume={6}, pages={3870-3873 vol.6} }

In numerous applications, such as communications, audio and music technology, speech coding and synthesis, antenna and transducer arrays, and time delay estimation, not only the sampling frequency but the actual sampling instants are of crucial importance. Digital fractional delay (FD) filters provide a useful building block that can be used for fine-tuning the sampling instants, i.e., implement the required bandlimited interpolation. In this paper an overview of design techniques and…

## 166 Citations

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- EngineeringIEEE Signal Processing Letters
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## References

SHOWING 1-10 OF 22 REFERENCES

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

- Computer ScienceIEEE Signal Process. Mag.
- 1996

This work presents a comprehensive review of FIR and allpass filter design techniques for bandlimited approximation of a fractional digital delay, focusing on simple and efficient methods that are well suited for fast coefficient update or continuous control of the delay value.

### A continuously variable digital delay element

- Engineering1988., 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.

### Offset windowing for FIR fractional-sample delay

- Geology1995 International Conference on Acoustics, Speech, and Signal Processing
- 1995

Non-optimal FIR filters used for fractional-sample delay, despite their wideband nature, are shown to benefit significantly from application of windowing, particularly if they are cast as asymmetric modifications of their conventional forms.

### Optimal two-term offset windowing for fractional delay

- Engineering
- 1996

Fractional-sample delay in discrete-time systems is often provided by special FIR filters which are asymmetric about mid-sequence. Here we preserve the appeal of sine-sequence fractional delayers…

### Evaluation of several variable FIR fractional-sample delay filters

- GeologyProceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing
- 1994

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.

### FIR approximation of fractional sample delay systems

- Mathematics
- 1996

This brief examines the approximation of fractional delays by FIR systems using various techniques which have previously been reported in the literature. In particular, the equivalence of the…

### Asymmetric Dolph-Chebyshev, Saramaki, and transitional windows for fractional delay FIR filter design

- Computer Science38th Midwest Symposium on Circuits and Systems. Proceedings
- 1995

An approach for the design of fractionally shifted (asymmetric) windows is presented, based on bandlimited sinc interpolation combined with oversampling techniques, demonstrating that shifting of symmetric windows can be achieved while essentially maintaining the magnitude response of the window spectrum.

### A simple design of maximally flat delay digital filters

- Mathematics
- 1972

The problem of maximally flat delay design of recursive digital filters has been solved by Thiran, using a direct z-domain approach. In this paper, the solution is obtained in a much simpler way by…

### Suppression of transients in variable recursive digital filters with a novel and efficient cancellation method

- EngineeringIEEE Trans. Signal Process.
- 1998

In this correspondence, the Zetterberg-Zhang algorithm is modified and the mean square error (MSE) measure for transients is defined and the optimal transient suppressor to cancel the transients down to a desired level at the minimum complexity of implementation.

### Discrete-Time Modeling of Acoustic Tubes Using Fractional Delay Filters

- Physics
- 1998

This work deals with digital waveguide modeling of acoustic tubes, such as bores of musical woodwind instruments or the human vocal tract, and a novel discrete-time signal processing technique, deinterpolation, is defined.