Complex Square Root with Operand Prescaling

We propose a radix-r digit-recurrence algorithm for complex square-root. The operand is prescaled to allow the selection of square-root digits by rounding of the residual. This leads to a simple hardware implementation of digit selection. Moreover, the use of digit recurrence approach allows correct rounding of the result if needed. The algorithm, compatible with the complex division presented in Ercegovac and Muller (“Complex Division with Prescaling of the Operands,” in Proc. Application-Specific Systems, Architectures, and Processors (ASAP’03), The Hague, The Netherlands, June 24–26, 2003), and its design are described. We also give rough estimates of its latency and cost with respect to implementation based on standard floating-point instructions as used in software routines for complex square root.

浮点倒数查找表的构造

在浮点除法器的设计中，若用函数迭代或高基数算法进行除法运算，计算开始时，通过浮点倒数查找表获得一个较精确的初始除数倒数近似值，可以减少除法的迭代次数，缩短运算的延迟。即将除数的前几位作为表的一个入口地址，该地址指示的位置存放着满足一定精度的初值倒数近似值。文中详述了几种获得除数倒数近似值的方法，其中包括算法、误差限和精度等。     

根升余弦脉冲成形滤波器FPGA实现

提出了基于电路分割技术实现通信系统发送端根升余弦波形成形滤波器查表法的FPGA结构,节省了ROM单元,讨论了其ROM初始化时形渡数据的组织方法,完成了该结构的VHDI。实现,给出了该设计在Modelsim环境下的时序仿真结果。通过对仿真结果分析,表明所述的设计方法是可行的。该设计方案不随波形样本数目的增多而使电路系统变得更为复杂,它所实现的成形滤波器满足于高速成形的应用需求。     

Error Analysis of the Kmetz/Maenner Algorithm

Use of low-precision logarithms can minimize power consumption and increase the speed of multiply-intensive signal-processing systems, such as FIR filters. Although straight table lookup is the most obvious way to compute the logarithm, Maenner claims to have discovered a technique that produces four extra bits at no cost. We analyze Maenner's technique and show that in fact the technique provides only one extra bit of precision. A related technique by Kmetz, which has never been analyzed before, is shown here to be more accurate than Maenner's. We compare these techniques to the more complex bipartite technique, and show that Kmetz's technique takes less memory for systems requiring fewer than ten bits of precision.     

成像系统均方根半径及调制传递函数的计算

本文给出了逸出电子在最佳像面上落点的均方根半径值及直观图形表示;以实际管型为例,βeta分布取β_1,8至β_2,1,检验了均方根半径的变化状况,证明了理论分析的正确性;从数据上检验了均方根半径不仅可以表征系统鉴别率特性的好坏,而且和调制传递函数的优劣在像面上是一一对应的;证明了用指数形式表示系统的调制传递函数具有计算速度快、形式简洁、使用方便,并且在低频空间具有足够的精度.