The Digital All-Pass Filter: A Versatile Signal Processing Building Block

The digital all-pass filter is a computationally efficient signal processing building block which is quite useful in many signal pmcessing applications. In this tutorial paper we review the properties of digital all-pass filters, and provide a broad overview of the diversity of applications in digital filtering. Starting with the definition and basic properties of a scalar all-pass function, a variety of structures satisfying the all-pass property are assembled, with emphasis placed on the concept of structural losslessness. Applications are then outlined in notch filtering, complementary filtering and filter banks, multirate filtering, spectrum and group-delay equalization, Hilbert transformations, and so on. In all cases, the structural losslessness property induces very robust performance in the face of multiplier coefficient quantization. Finally, the state-space manifestations of the all-pass property are explored, and it is shown that many all-pass filter structures are devoid of limit cycle behavior and feature very low roundoff noise gain.