Design and implementation of variable digital filters with low computational complexity
Xu, Wei Jing
Date of Issue2014
School of Electrical and Electronic Engineering
Variable digital filters (VDFs) have various applications in digital communications, sampling rate conversion, array signal processing, etc. The useful variable characteristics of digital filters include variable bandedges and variable fractional delays (VFDs). However, the computational complexity of VDFs is usually higher than that of the filters with fixed characteristics. The objective of this research is to investigate the design and implementation of VDFs with low computational complexity. Same as the fixed filter design, there are closed-form approaches and numerical optimization techniques available for the design of VDFs. In this thesis, both the closed-from approach and numerical optimization techniques are studied. In the closed-form design, the Lagrange interpolation, implemented in the Farrow structure, is one of the popular approaches for the design of VFD filters and the researches are focused on the reduction of the computational complexity by using matrix transformations. In this thesis, the dependance between the subfilter coefficients of the Lagrange interpolation is investigated and discovered. An efficient implementation structure making use of the coefficient dependance was proposed to significantly reduce the computational complexity. While the closed-form VFD filters are convenient to design, it can achieve VFD only for a narrow frequency range. When wider variation range and more accurate control on the variable characteristics are required, numerical optimization techniques are generally adopted. In numerical optimizations, an objective function is minimized subject to some constraints. In the existing researches, the objective functions to be minimized include frequency response error, phase error, phase delay error and group delay error. However, in the most common applications of the VFDs, the time domain instantaneous delayed samples are estimated. In this thesis, for such applications, the relations between the above frequency domain errors (in particular the frequency response error, phase error and group delay error), and the time domain errors are investigated. The design criteria of the VFD filters for this particular application are identified. Besides the investigation on the design criteria, a new VFD filter design approach is proposed. In this approach, the full band input signal is split into several subbands by a newly proposed filter bank. By shifting each subband a proper phase, the VFD is realized by combining necessary subbands. The proposal VFD technique can be incorporated with the variable bandedge characteristic with little extra complexity. Hence, the filters with simultaneously variable bandedges and fractional delays (VBFDs) are obtained. In the design of the VBFD filters, the split subbands can be either kept or discarded to form the variable bandedges. However, this requires the bandwidth of the individual band of the filter bank to be narrower than the transition bandwidth of the VBFD filters. By introducing a shaping filter to the last retained band to form the transition band of the VBFD filters, the bandwidth of the individual band of the filter bank may be relaxed to about twice of the transition bandwidth of the VBFD filters. Compared with the existing VBFD filter design techniques, the proposed approaches significantly reduce the computational complexity of the VBFD filters.
DRNTU::Engineering::Electrical and electronic engineering::Electronic systems::Signal processing