【摘要】 ＦＩＲ数字滤波器（ＦＩＲＤＦ）软件设计方法一般采用Ｆｏｕｒｉｅｒ级数法、频率抽样法和切比雪夫最佳一致逼近法．由于常规ＦＩＲＤＦ设计方法的自身特点，要取得通带、阻带和过渡带性能都最优的滤波器很困难，并且难以实现灵活可调的多通带（阻带）线性相位滤波器．文中分析了ＦＩＲＤＦ的特点之后，根据小波理论中连续小波变换的性质和函数逼近理论，提出了ＦＩＲＤＦ设计的新方法——小波逼近方法．利用多个小波函数来逼近理想滤波器的频率特性．结果表明，ＦＩＲＤＦ设计的小波方法比切比雪夫逼近法和离散小波变换共轭镜象滤波器方法，其计算过程更灵活，带宽选择更方便，计算速度更快．根据不同的滤波要求，很容易设计多通带的带通滤波器和多通带移相器．更多还原

【Abstract】 In order to reduce the gibbs and ripples of FIR DF, the Windowed Fourier Series and Chebyshev Approximation are preferably used to design filters. It is difficult to conveniently design multipassband linear phase optimum filters because of the complicated procedures of these two approaches. Quadrature Mirror Filter based discrete wavelet decomposition provides an alternative method for multipassband signal filtering, but this signal decomposition approach can not be used to design 90 degree phaseshift filters. Based on the frequency localization of continuous wavelet transform and approximation theory, this paper presents a new approach to the design of FIR digital filters, wavelet approximation approach, to approximate the ideal magnitudefrequency properties by the combination of wavelets. It is found the wavelet approximation approach, compared with the Chebyshev approximation and Quadrature Mirror Filter based discrete wavelet decomposition, contains the features of easier filter design and faster computing speed. Furthermore, the signal can be easily multipassband filtered and the Hilbert transform for the band passed signal is implemented at the same time.更多还原