Fractional delay (FD) filters are fundamental in digital signal processing when signals must be delayed by a non-integer number of samples with high accuracy and low distortion. Applications include sample rate conversion, beamforming, synchronization, and channel modeling. Among the various FD filter design methods, the Farrow structure has emerged as a particularly efficient and flexible approach. This presentation introduces the principles, implementation, and advantages of fractional delay Farrow filters.

We begin by reviewing the concept of FD filtering and the challenges associated with achieving arbitrary delays in discrete-time systems. Next, the Farrow filter structure is examined in detail, highlighting its polynomial-based decomposition and modular architecture that enables real-time tunability of the delay without redesigning the filter. The computational benefits of the Farrow approach, including its suitability for hardware implementation and low memory footprint, are discussed.

Simulation examples demonstrate the performance of different polynomial approximations in terms of delay accuracy, group delay distortion, and numerical stability. Finally, we outline practical applications where fractional delay Farrow filters offer significant performance gains. Attendees will gain a clear understanding of both the theoretical foundations and practical aspects of these filters, equipping them to apply Farrow structures effectively in DSP systems.