The Short Time Spectra Analysis System Using The Complex LMS Algorithm and It's Applications

B.Widrow established fundamental relations between the least-mean-square (LMS) algorithm and the digital Fourier transform［1］. By extending these relations, we proposed the short time spectra analysis system using the LMS algorithm［2]. In that paper, we used the normal LMS algorithm on the thought of dealing with only real analytical signal. This algorithm minimizes the real mean-square by recursively altering the complex weight vector at each sampling instant. But, the short time spectra analysis sometimes deals with the complex signal that is outputted from complex analog filter. So, in order to optimize and develop this methods, furthermore it is necessary to derive an algorithm for the complex analytical signal. In this paper, we first discuss the new adaptive system for the spectra analysis using the complex LMS algorithm and then derive convergence condition, time constant of coefficient adjustment and frequency resolution by extending the discussion. Finally, the effectiveness of the proposed method is experimentally demonstrated by applying it to the measurement of transfer performance on complex analog filter.