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In the field of measurement signal processing, we should often change the characteristic of the stopband instantaneously. Such the filter that can change the frequency response instantaneously is called variable filter. We propose the design of FIR digital filters with variable stopbands. In this paper, the quasi-chebyshev characteristic is obtained by using an iterative weighted least square (WLS) method. Moreover, a memory required for the calculation for computing filter coefficients in the proposed method has the feature of being fewer than the conventional method. The usefulness of the proposed design method is verified through some examples.