Unitary and paraunitary matrices have found a number of applications in signal processing. A paraunitary matrix H(z) in the complex field is nothing but a rational function of z (with complex coefficients), which is unitary for z=e/sup jw/. When computations are performed in a finite field, it is important to deal with this class of matrices in a finite field. Unitary and paraunitary matrices in finite fields are introduced. Various properties are studied, including the possibility of factorizations in terms of Householder building blocks. For the case of FIR (finite impulse response) systems, state-space manifestation of the paraunitary property is also considered.
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机译:ary和超unit矩阵已经在信号处理中找到了许多应用。复数域中的超unit矩阵H(z)只是z(具有复数系数)的有理函数,它对于z = e / sup jw /是unit一的。在有限域中执行计算时,在有限域中处理此类矩阵非常重要。介绍了有限域中的矩阵和超unit矩阵。研究了各种属性,包括就Householder构造块而言进行因式分解的可能性。对于FIR(有限脉冲响应)系统,还考虑了准unit性质的状态空间表现。
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