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This paper describes a method of designing the fan filter with a steep cutoff characteristic, using McClellan transformation. The conventional design by McClellan transformation has a problem in that the cutoff region of the fan filter is broad due to the restriction to a lower order of the subfilter employed. From such a viewpoint, this paper proposes a systematic design method for the subfilter with arbitrary order. First, it is pointed out that the ideal response of the subfilter can be represented in a functional form. Then the error function is defined in regard to the ideal response, and the design is shown for the subfilter where the filter coefficients minimize the error function. Finally, a design example is discussed, and it is shown that a fan filter with a steeper cutoff characteristic than in the conventional method can be designed by the proposed method.

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It is important from the viewpoint of economy to realize the digital filter with as little hardware complexity as possible. On the other hand, the theory of low‐sensitivity FIR filter is not advanced, compared with that of the IIR filter. From the viewpoint of minimizing the coefficient word‐length, an investigation of this problem is required. With this as background, this paper aims at the reduction of the coefficient wordlength of the multiplier, and proposes the cascade construction of the FIR filter. First, using the coefficient sensitivity, an evaluation function is defined and used to evaluate the degradation of response due to the coefficient quantization. Then the relation between the locations of zeros and the value of the evaluation function is discussed. It is pointed out that the zeros with relatively remote locations reduce the response degradation. A systematic construction of the low‐sensitivity structure is described, considering the relation between the location of zeros and the evaluation function. Finally, to show its effectiveness, several examples are handled by the proposed method.

The cause of the error in the FFT is due mostly to the quantization error of the input data, the round‐off error in arithmetic operation, and the computation error of Wnk= exp (‐j 2nk /N). of these, the error of Wnk is complex, and this error is approximated in the reported error analysis by the truncation error by finite bits. This paper examines the actual computation error of Wnk and its effect. As a result, it is shown that the computation error of Wnk is much larger than the truncation error by the finite bits, and can produce instability in the algorithm. Then to solve the problem, this paper proposes a method to improve the computation accuracy of Wnk. the proposed method can be executed without increasing greatly the processing time and the memory, compared with the direct FFT computation. By using the proposed processing, the error analysis is made more reliable than in the past and the error accompanying the FFT is reduced. Finally, the effectiveness of the proposed method is verified by several examples.