Efficient convolution algorithms with an FIR representable as a spline

The convolution is calculated in the case when the finite impulse response can (FIR) be representable as a spline. This approach is a practical illustration of the method proposed in 4, 5] for constricting an efficient convolution algorithm. A brief theoretical justification of the approach is given. An efficient convolution algorithm for a Gaussian FIR is constructed as an example and is compared with other convolution algorithms. Vladislav Valer’evich Myasnikov. Born 1971. Graduated from the Samara State Aerospace University (SSAU) in 1994. Began his graduate study at SSAU in 1995 and received candidate’s degree in technical sciences in 1998. Senior researcher at the Image Processing Systems Institute of the Russian Academy of Sciences and associate professor at the SSAU Department of Geoinformatics. Research interests: digital signal and image processing, geoinformatics, neural networks, and pattern recognition. Author of more than 60 publications, including 24 papers and 1 monograph (coauthored). Member of the Russian Association for Pattern Recognition and Image Analysis. Ol’ga Aleksandrovna Titova. Born 1980. Graduated with honors from the Samara State Aerospace University in 2003. Graduate student at SSAU from 2003 to 2006. Assistant professor at the SSAU Department of Geoinformatics. Research interests: digital processing of signals and images, including remote sensing data; geoinformation systems; and pattern recognition. Author of 19 publications, including 4 papers. Member of the Russian Association for Pattern Recognition and Image Analysis.