Summary: This paper proposes algorithms for decomposing digital filters into a combination of very simple standard elements. Device realization of such filters ensures high-speed digital signal processing. Section 1 treats an algorithm for approximating digital filter kernels by discrete splines which can be represented by convolutions of simple piecewise-constant functions. The use of these splines reduces the number of arithmetic operations considerably as compared with the standard convolution method. Section 2 proposes a method of decomposing digital filter kernels into a convolution of one-type components concurrently computable at low cost. Section 3 describes a special algorithm for decomposing reject-type filters by using simple local kernels. Section 4 treats the problem of decomposing nonstationary filters into simple components, which is solved by well-known methods developed for stationary filters.