理想数字滤波器的谐波小波逼近模型与设计方法

分析谐波小波的频域特征和滤波特性，研究理想数字滤波器的谐波小波逼近模型与实现方法。利用谐波小波在频域具有良好的紧支特性和盒形特性，建立理想数字滤波器的小波逼近模型。通过谐波小波变换，实现逼近滤波器的带宽和中心频率的可调。该逼近滤波器的幅频特性已逼近理想数字滤波器的幅频特性，且具有零相移特性，并通过傅里叶变换实现其快速算法。通过算例和工程应用实例验证，该方法能有效地滤除噪声信号，具有算法简捷、快速等特点，能对实测信号进行实时滤波。

APPROACH MODELING AND DESIGN METHOD FOR IDEAL DIGITAL FILTER USING HARMONIC WAVELET TRANSFORMS

The principle and algorithm of a new approach to the ideal digital filter using harmonic wavelet transforms are introduced, and the characteristics in frequency domain and filtering capability of harmonic wavelets are analyzed. Using the box-like spectrum of harmonic wavelets in frequency domain, a new approach modeling to the ideal digital filter by using har-monic wavelet transforms is established. The bandwidth and central frequency of this approach filter are adjusted with har-monic wavelet transforms. The amplitude-frequency character-istics of the approach filter are close to the ideal digital filter, and have zero-phase characteristic. The fast algorithm of this approach filter is realized by Fourier transform. Examples of application demonstrate that this method presented can effec-tively filter the noise from the signal. This method is also fea-tured by simple algorithm, fast and real time performing in application as well.