If you want to delay a discrete-time signal by a non-integer multiple of the sampling time, you should use a fractional delay filter. The performance of a fractional delay filter depends on how to reconstruct inter-sample responses. The paper proposes a new design method based on sampled-data H-infinity optimization, which is superior to standard Shannon-based filters.

## Why is it important?

Fractional delay filters have wide applications in signal processing; sampling rate conversion, nonuniform sampling, wavelet transform, digital modeling of musical instruments, to name a few. The paper gives an optimal design procedure that optimizes analog performance of signal reconstruction. This is very important for many applications since their performance is measured in analog domain (e.g. sound quality is determined when the sound comes out from loudspeakers).

This page is a summary of: $H^{\infty}$ -Optimal Fractional Delay Filters, IEEE Transactions on Signal Processing, September 2013, Institute of Electrical & Electronics Engineers (IEEE), DOI: 10.1109/tsp.2013.2265678.