This paper proposes a new angular measurement system to a moving target in the presence of clutter. We apply MUSIC (MUltiple SIgnal Classification) to the outputs of a Doppler filter bank consisting of quadrature mirror filter (QMF). The comparison between QMF and the short time Fourier transform (STFT) as a preprocessor of MUSIC is also discussed. DOA estimation performance by QMF-MUSIC is nearly equal to that of STFT-MUSIC. On the other hand, QMF-MUSIC overcomes STFT-MUSIC in the aspect of computational cost. In a specific example in this paper, the proposal QMF bank by Daubechies (4th order) wavelet requires 80% fewer the number of multiplications and 25% fewer the number of additions than the FFT-based STFT filter bank.