All Phase FIR Filter Banks

First, based on the architecture of the APDFT filter, this paper brings out a newtype of zero-phase digital filter called the windowed all phase DFT (WAPDFT)digital filter, by windowing the input and/or output data of the DFT/IDFT blocks inthe APDFT filter network. The frequency characteristics of the APDFT filter areimproved greatly by this way. While the frequency response of the filter still passes orapproaches the desired frequency samples, it has much less pass-band and stop-bandripples, and sharp transition. The WAPDFT filter can be implemented with commonconvolution structure and the frequency domain direct network like the APDFT filter,and realized in a simplified structure also. This paper gives the network of the newstructure and the associate algorithm. This network is not sensitive to finite wordlength effect compared with traditional frequency sampling structures. It has real-timeself-design function and may constitute a time-variant system. It can be easilyintegrated into a universal zero-phase digital filter with frequency response and lengthprogrammable.Second, this paper proposes a new type of half band filter—the all phase halfband filter (APHF). It has the property of frequency sampling, i.e. the response curvepasses desired frequency samples. Its frequency response has very small pass-bandripple, great stop-band attenuation, sharp transition band and without overshootingwhether in stop-band or pass-band. It can be used to design two-channel perfectreconstruction QMF (quadrature mirror filter) banks by factorizing the spectrum forthe APHF directly. A new method is given to get the spectral factors of the APHFwith high precision. Compared with traditional spectral factorization method ofdesigning two-channel perfect reconstruction QMF banks, the QMF banks designedby factorizing APHF has better reconstruction precision that the error is decreasedfrom 10?3dB to10?6dB. It's a new method for designing half band filters andtwo-channel perfect reconstruction QMF banks.Finally, using the WAPDFT filter design method, this paper proposes an allphase M band filter with all the advantages mentioned above and an all phase uniformDFT filter bank. The uniform DFT filter bank can be used to time-frequencyanalysis—windowed fourier transform. Although wavelet transform is a useful toolfor time-frequency analysis, it is not suitable for analysing linear charp signals.Whereas, the all phase uniform DFT filter bank can do it very well duo to thewindowed all phase can efficiently reduce the side lobes of the window.