Several existing algorithms for multiplication of large integers are discussed, and a highly efficient algorithm based on finite discrete convolution is introduced. In the new algorithm, large integers are split into many digits and stored in arrays, every item in array stands for every digit of large integer. In this way, the integer can be any large; the only limit is the memory of computer. ...

The problem of robust stability analysis for uncertain discrete singular time-delay systems is investigated in this paper. By decomposing the nominal system into slow and fast subsystems, a linear matrix inequality (LMI) condition is proposed for a discrete singular time-delay system to be regular, causal and stable. Based on this, an LMI criterion is obtained for robust stability of an uncerta...

Convolution is one of the most widely used digital signal processing operations. It can be implemented using the fast Fourier transform (FFT), with a computational complexity ofO(N logN). The undecimated discrete wavelet transform (UDWT) is linear and shift invariant, so it can also be used to implement convolution. In this paper, we propose a scheme to implement the convolution using the UDWT,...