1. A signal-processing apparatus comprising: a first Discrete Fourier Transform unit including a real number input portion and an imaginary number input portion, in which each component in a first time window of a first series of input signals in time domain and each component in a second time window of a second series of input signals in time domain are fed into said first Discrete Fourier Transform unit through said real number input portion and said imaginary number input portion, respectively, said first Discrete Fourier Transform unit being operable to transform the components entered through said real number and imaginary number input portions into a complex number data vector in frequency domain; a vector-multiplying unit operable to provide a a calculation result; and an Inverse Discrete Fourier Transform unit including a real number output portion and an imaginary number output portion, said Inverse Discrete Fourier Transform unit being operable to inversely transform the calculation result, thereby feeding first and second series of output signals in time domain out of said Inverse Discrete Fourier Transform unit through said real number output portion and said imaginary number output portion, respectively, wherein said vector-multiplying unit comprises a splitter operable to separate the complex number data vector into a first data and a second data, said vector-multiplying unit provides the calculating result for each of: the first data, the second data, a first complex number coefficient vector, and a second complex number coefficient vector, wherein the first complex number coefficient vector includes a coefficient vector obtained by discrete Fourier transforming a first convolution coefficient of real number in time domain and a second convolution coefficient of imaginary number in time domain, wherein the second complex number coefficient vector includes a coefficient vector obtained by discrete Fourier transforming a third convolution coefficient of real number in time domain and a fourth convolution coefficient of imaginary number in time domain.