A design of vector filter banks

Vector filter banks (VFB´s) can represent filter banks using a block sampling and the vector transforms. They are also appropriate to vector quantization. In the conventional study of VFB´s, their polyphase representations and perfect reconstruction (PR) conditions have been given. However, no design method for VFB´s has been given. This paper proposes a design method for VFB´s using DFT modulation. First, we derive a polyphase representation using DFT modulation where the block size is the multiple of the number of channels. The efficient matrix representations are also presented in which the FFT algorithm can be used. Next, we propose a realization method for PR. We show that PR conditions are described by linear equations, and PR can be realized using larger-length analysis filters compared with that of scalar DFT modulated FIR filter banks. Finally, we show a design example of proposed VFB´s