sine transform
3.In this paper the fast recursive algorithm for the one-di-mensional discrete sine transform-Ⅱ(1-D DST-Ⅱ) suggested in [6] is extended to two dimensions using the vector-radix decomposition to obtain a fast algorithm for decimation-in-frequency, (2m×2m) -point,vector-radix,two-dimensional discrete sine transform-Ⅱ.
6.Then, a semi-analytical solution for the velocity response of the pile subjected to a semi-sine wave exciting force was derived by using invert Fourier transform.
9.By employing the Fourier Bessel theorem to plane wave functions and through a series of deduction and inverse Fourier transform,one kind of series expansions of the product of Bessel functions and sine/cosine function in Cartesian coordinates is obtained. This expression can be used to compute the rectangular to circular waveguide junction and to analytically deduce its generatized S parameters,which are in good agreement with results from other papers and HFSS.

