2017
DOI: 10.1007/s10851-017-0758-9
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Fast Recursive Computation of Krawtchouk Polynomials

Abstract: Krawtchouk polynomials (KPs) and their moments are used widely in the field of signal processing for their superior discriminatory properties. This study proposes a new fast recursive algorithm to compute Krawtchouk polynomial coefficients (KPCs). This algorithm is based on the symmetry property of KPCs along the primary and secondary diagonals of the polynomial array. The n−x plane of the KP array is partitioned into four triangles, which are symmetrical across the primary and secondary diagonals. The propose… Show more

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Cited by 42 publications
(47 citation statements)
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“…Obviously, in the proposed method, the average execution time to generate DKPCs is less than existing methods. This achievement is due to: (1) the proposed method computed only 12.5% of the DKPCs, and (2) a reduced complexity forms of the existing recurrence relations are introduced (Equations (11) and (13)). To affirm the results of the proposed algorithm, the improvement ratio of the execution time is measured.…”
Section: Performance Evaluation Of the Proposed Methodsmentioning
confidence: 99%
See 2 more Smart Citations
“…Obviously, in the proposed method, the average execution time to generate DKPCs is less than existing methods. This achievement is due to: (1) the proposed method computed only 12.5% of the DKPCs, and (2) a reduced complexity forms of the existing recurrence relations are introduced (Equations (11) and (13)). To affirm the results of the proposed algorithm, the improvement ratio of the execution time is measured.…”
Section: Performance Evaluation Of the Proposed Methodsmentioning
confidence: 99%
“…The proposed method is also evaluated in terms of maximum size can be generated and compared to that of the existing methods. For each method, the maximum size is found using the procedure presented in [13]…”
Section: Performance Evaluation Of the Proposed Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…Different TTR algorithms have been proposed [11], [16]. In this study, the TTR algorithm, which was proposed by [15], is used. In this TTR algorithm, the KP plane is divided into four triangular parts bounded by primary and secondary diagonals, as shown in FIGURE 1.…”
Section: B Krawtchouk Orthogonal Polynomialmentioning
confidence: 99%
“…The difference between transforms is determined by the type of the transform (polynomial) basis function. Basis functions are used to extract significant features of signals [ 114 ]. For example, DFT uses a set of complex and natural harmonically related exponential functions, whereas DCT is based on a cosine function with real values from to 1.…”
Section: Sbd Approachesmentioning
confidence: 99%