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A new method named prediction-correction homotopy method is proposed to calculate Hopf bifurcation points associated with the parameter dependent differential algebraic equations (DAE) which are used to model power systems dynamics. It uses the secant prediction method to track the Hopf bifurcation homotopy path. Compared with the tangent prediction method, the computation load is much less because it is not related to the matrix inversion computation. At the same time, the automatic step-size control strategy ensures the calculation accuracy and speed to effectively implement the stepby-step correction. Finally, it is proved that this algorithm can be used accurately and effectively through WSCC 3-machine 9-bus system and NewEngland 39-bus system.

Channelization is one of the most important parts in a Digital Back-End(DBE) for radio astronomy. A DBE with wider bandwidth and higher resolution consumes larger amount of computing and memory resources, which results in much higher hardware cost. This paper presents an efficient channelization architecture, which consists of Bit-Inverted, Parallel Complex Fast Fourier Transform(BIPC-FFT) and In-place Forward-Backward Decomposition(IPFBD). The efficient architecture can assist with saving a lot of resources, so a wide-band and high-resolution DBE can be implemented on an resource restricted platform. Based on the efficient channelization architecture, we designed a Dual-Input, 64K-Channelized prototype DBE with 1.2 GHz bandwidth on a Xilinx Virtex-6 LX240T Field Programmable Gate Array(FPGA) chip. The test results in the lab and observation results at Yunnan Observatory demonstrate the DBE can be used for radio astronomy.

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