Abstract
In this paper a numerically efficient method for designing a nearly optimal variable fractional delay (VFD) filter based on a simple and well-known window method is presented. In the proposed method a single window extracted from the optimal filter with fixed fractional delay (FD) is divided into even and odd part. Subsequently, the odd part is discarded and symmetric even part of the extracted window is used to design a family of nearly optimal filters with varying FD. In addition to window extraction, the proposed approach requires filter gain correction which is dependent on the desired FD. Optimum values of the gain correction factor as well as the extracted window can be computed beforehand, which allows us to design a nearly optimal FD filter with arbitrary FD at low numerical costs during runtime. On the basis of the proposed filter design method, the universal structure of VFD filter allowing for change of filter type and length has been proposed. In the paper, three FD filter optimality criteria are considered, which are maximal flatness, Chebyshev (minimax), and least squares.
Highlights
In many digital signal processing applications, such as synchronization in digital modems [14,37], incommensurate sampling rate conversion [8,15,20,29], and speech coding [9,26], there is a necessity for delaying signals
In the paper we have demonstrated that nearly optimal minimax and least squares (LS) filters can be designed using symmetric window method with practically negligible errors of the order of 0.01 dB or smaller
In this approach only a single window is required to design the entire family of fractional delay (FD) filters differing only in FD
Summary
In many digital signal processing applications, such as synchronization in digital modems [14,37], incommensurate sampling rate conversion [8,15,20,29], and speech coding [9,26], there is a necessity for delaying signals. The simplicity of the window method makes it ideal for VFD filter design but the selection of window satisfying given specifications is usually difficult This is why a filter design using the window method requires an iterative approach which still often produces results significantly worse than optimal. The presented research is based on the concept of an extracted window proposed in [17], where even length nearly optimal minimax FD filters are designed using a window extracted from a symmetric FD filter with the FD dref = 0.5. We have proposed a formula for direct calculation of gain correction factor for all required delays based only on a single reference window, without the need for optimal filters design.
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