Study On Perfect Reconstruction QMF Banks And Its Application In A/D Conversion

Software radio which promises well needs a kind of wideband high speed and resolution ADC, but at present it is hard to realize. On the basis of the theory of multirate signal processing, the theory of filters, bandpass sampling theorem and ADC principium, Perfect Reconstruction Quadrature Mirror Filter (PRQMF) banks ADC system is proposed. The principle, structure and characteristics of the ADC system has been discussed and studied, the main conclusions and contributions include:The general Perfect Reconstruction (PR) condition of linear phase PRQMF banks is deduced mathematically, which consists of combination relation between analysis filter's odd length or even length and its symmetry or antisymmetry, relation of analysis filters' lengths and relation of the coefficients among different analysis filters. On the basis of the general PR condition, the nonlinear optimization solution of linear phase PRQMF banks is studied deeply with Sequential Quadratic Programming (SQP). SQP Solution steps of M-channel PRQMF banks are given, and in which the differential problems are discussed in details.Frequency response, quantization noise, reconstruction error and its sensitivity to mismatch among ADCs are studied at length in PRQMF banks ADC system, and the theoretic results include: (1) the distortion /aliasing functions of hybrid filter banks ADC system is similar with that of Switch Capacitor filter banks ADC system; (2) for wide or narrow band input signal, the effective resolution of the two ADC systems is 0.51og2M bits higher than their ADC; (3) reconstruction error's sensitivity to mismatch among ADCs of the two ADC systems is reduced effectively than time interleaved ADC system.The bottleneck of hybrid filter banks ADC system is that it cannot sample directly higher radio frequency signal because of lower analog input bandwidth of its ADC. In order to remove it, a kind of downsampler model based on Nyquist and bandpass sampling theorem is presented, analyzed and proved in time and frequency domain, in addition a downsampler is designed according to the model. On the basis of hybrid filter banks ADC system, a class of high speed hybrid filter banks ADC system is proposed.On the basis of high speed hybrid filter banks ADC system, a kind of downsampler model based on bandpass sampling theorem is presented, and analyzed, proved in time and frequency domain, in addition a downsampler is designed according to the model. A class of high effective hybrid filter banks ADC system which bases on the downsampler and radio frequency spectrum is proposed, of which digital signal rate falls M times as fast as the former. By simplifying the ADC system, a specific kind of high effective hybrid filter banks ADC system is proposed too. Furthermore, result of quantization noise shows that the effective resolution is 0.51og2M bits higher than its ADC in the ADC system.Due to low effective resolution of time interleaved ADC system, a class of high-speed-and-resolution time interleaved ADC system is proposed. The effective resolution of the ADC system is 0.51og2M bits higher than the former.Linear phase PRQMF banks is one of focal points in multirate digital signal processing domain, its general PR condition is deduced mathematically in the paper, which is important for further studying its design method, in addition high speed hybrid filter banks ADC system , high effective hybrid filter banks ADC system and high-speed -and-resolution time interleaved ADC system proposed in the paper have practical value.