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Masayoshi Nakamoto,Takao Hinamoto,Shuichi Ohno 대한전자공학회 2009 ITC-CSCC :International Technical Conference on Ci Vol.2009 No.7
In this paper, we propose a new FIR filter structure which consists of the shift operation circuits and single multiplier. Though the approximate accuracy for the required frequency response is not better than that of the general FIR filters, the processing speed is higher because most calculation is the shift operation in this structure. The error caused by the change of filter coefficients distributes in the stop-band, so the sharp cutoff characteristic can be retained. Of course, the stability and linear phase characteristic of the filter is also preserved. Also, we show the algorithms for designing the proposed FIR filters. For designing the single multiplier, the Lagrange multiplier method is used, and for optimization of the shift operation circuits, we propose the branch and bound based algorithm. Finally, we show the effectiveness of the proposed method by using the numerical example.
Masayoshi Nakamoto,Yuuki Hayakawa,Yutaka Kurumaji,Takao Hinamoto 대한전자공학회 2008 ITC-CSCC :International Technical Conference on Ci Vol.2008 No.7
In this paper, we formulate the filter design problem based on modified least square criterion in the frequency domain. Here the problem is expressed as quadratic form and we optimize the filter coefficients by using branch and bound method in discrete space. In the branch and bound method, we calculate the relaxation solution based on the Lagrange multiplier method and search in the domain in which good possible solutions exist. In this method, the stable solutions whose poles are all inside the unit circle are just acceptable, so the stability of the filter can be guaranteed. Finally, numerical example is given to illustrate the utility of the proposed method.