Symmetric Structures for Odd-Order Maximally Flat and Weighted-Least-Squares Variable Fractional-Delay Filters

Pascal-Interpolation-Based Noninteger Delay Filter and Low-Complexity Realization

“…This paper develops a new design method and a new realization structure for the causal polynomial-interpolation-type delay filter with very low hardware complexity in order to achieve high-speed filtering for real-time applications. As compared with the methods proposed in [10][11][12][13], the method proposed in this paper requires much less multiplications. The resulting filter structures from the methods in [10][11][12][13] require more multiplications than the Pascal structure proposed in this paper.…”

“…As compared with the methods proposed in [10][11][12][13], the method proposed in this paper requires much less multiplications. The resulting filter structures from the methods in [10][11][12][13] require more multiplications than the Pascal structure proposed in this paper. As compared with the existing methods for deriving and realizing the causal polynomial-interpolation-type delay filters, we develop a novel design method and a new filter structure using different procedures, but the resulting structure has much lower complexity.…”

“…Since the tunable noninteger-delay filter can change its non-integer group delay or phase delay, it can be applied to many fields of signal processing like one dimensional signal interpolation, sampling-rate conversion and image interpolation. So far, many design methods have been developed in the literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Among those existing filters, the polynomial-interpolation-type nonintegerdelay filter has simple and unique features.…”

“…Its amplitude response is the maximally flat for zero frequency. The derivation and realization of the polynomial-interpolationtype noninteger-delay filter have been dealt with in [9][10][11][12][13]. The most straightforward realization of the polynomialinterpolation-type noninteger-delay filter is to use the di-rect-form Farrow structure [1].…”

“…In order to perform real-time filtering, causal filters are needed, but the direct-form Farrow structure of the causal polynomialinterpolation-type noninteger-delay filters does not possess symmetric or anti-symmetric structures, which cannot exploit symmetries for reducing the number of multiplication operations. In [11][12][13], transformation matrices have been proposed for transforming causal filters to have lowcomplexity structures. This paper develops a new design method and a new realization structure for the causal polynomial-interpolation-type delay filter with very low hardware complexity in order to achieve high-speed filtering for real-time applications.…”