Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters

Two perfect-reconstruction structures for the two-channel quadrature mirror filter (QMF) bank, free of aliasing and distortions of any kind, in which the analysis filters have linear phase, are described. The structure in the first case is related to the linear prediction lattice structure. For the second case, new structures are developed by propagating the perfect-reconstruction and linear-phase properties. Design examples, based on optimization of the parameters in the lattice structures, are presented for both cases

Cyclic LTI systems in digital signal processing

Cyclic signal processing refers to situations where all the time indices are interpreted modulo some integer L. In such cases, the frequency domain is defined as a uniform discrete grid (as in L-point DFT). This offers more freedom in theoretical as well as design aspects. While circular convolution has been the centerpiece of many algorithms in signal processing for decades, such freedom, especially from the viewpoint of linear system theory, has not been studied in the past. In this paper, we introduce the fundamentals of cyclic multirate systems and filter banks, presenting several important differences between the cyclic and noncyclic cases. Cyclic systems with allpass and paraunitary properties are studied. The paraunitary interpolation problem is introduced, and it is shown that the interpolation does not always succeed. State-space descriptions of cyclic LTI systems are introduced, and the notions of reachability and observability of state equations are revisited. It is shown that unlike in traditional linear systems, these two notions are not related to the system minimality in a simple way. Throughout the paper, a number of open problems are pointed out from the perspective of the signal processor as well as the system theorist

Channelization for Multi-Standard Software-Defined Radio Base Stations

As the number of radio standards increase and spectrum resources come under more pressure, it becomes ever less efficient to reserve bands of spectrum for exclusive use by a single radio standard. Therefore, this work focuses on channelization structures compatible with spectrum sharing among multiple wireless standards and dynamic spectrum allocation in particular. A channelizer extracts independent communication channels from a wideband signal, and is one of the most computationally expensive components in a communications receiver. This work specifically focuses on non-uniform channelizers suitable for multi-standard Software-Defined Radio (SDR) base stations in general and public mobile radio base stations in particular. A comprehensive evaluation of non-uniform channelizers (existing and developed during the course of this work) shows that parallel and recombined variants of the Generalised Discrete Fourier Transform Modulated Filter Bank (GDFT-FB) represent the best trade-off between computational load and flexibility for dynamic spectrum allocation. Nevertheless, for base station applications (with many channels) very high filter orders may be required, making the channelizers difficult to physically implement. To mitigate this problem, multi-stage filtering techniques are applied to the GDFT-FB. It is shown that these multi-stage designs can significantly reduce the filter orders and number of operations required by the GDFT-FB. An alternative approach, applying frequency response masking techniques to the GDFT-FB prototype filter design, leads to even bigger reductions in the number of coefficients, but computational load is only reduced for oversampled configurations and then not as much as for the multi-stage designs. Both techniques render the implementation of GDFT-FB based non-uniform channelizers more practical. Finally, channelization solutions for some real-world spectrum sharing use cases are developed before some final physical implementation issues are considered

Practical Non-Uniform Channelization for Multistandard Base Stations

A Multistandard software-defined radio base station must perform non-uniform channelization of multiplexed frequency bands. Non-uniform channelization accounts for a significant portion of the digital signal processing workload in the base station receiver and can be difficult to realize in a physical implementation. In non-uniform channelization methods based on generalized DFT filter banks, large prototype filter orders are a significant issue for implementation. In this paper, a multistage filter design is applied to two different non-uniform generalized DFT-based channelizers in order to reduce their filter orders. To evaluate the approach, a TETRA and TEDS base station is used. Experimental results show that the new multistage design reduces both the number of coefficients and operations and leads to a more feasible design and practical physical implementation

Practical Non-Uniform Channelization for Multistandard Base Stations

A Multistandard software-defined radio base station must perform non-uniform channelization of multiplexed frequency bands. Non-uniform channelization accounts for a significant portion of the digital signal processing workload in the base station receiver and can be difficult to realize in a physical implementation. In non-uniform channelization methods based on generalized DFT filter banks, large prototype filter orders are a significant issue for implementation. In this paper, a multistage filter design is applied to two different non-uniform generalized DFT-based channelizers in order to reduce their filter orders. To evaluate the approach, a TETRA and TEDS base station is used. Experimental results show that the new multistage design reduces both the number of coefficients and operations and leads to a more feasible design and practical physical implementation

An Efficient Polyphase Filter Based Resampling Method for Unifying the PRFs in SAR Data

Variable and higher pulse repetition frequencies (PRFs) are increasingly being used to meet the stricter requirements and complexities of current airborne and spaceborne synthetic aperture radar (SAR) systems associated with higher resolution and wider area products. POLYPHASE, the proposed resampling scheme, downsamples and unifies variable PRFs within a single look complex (SLC) SAR acquisition and across a repeat pass sequence of acquisitions down to an effective lower PRF. A sparsity condition of the received SAR data ensures that the uniformly resampled data approximates the spectral properties of a decimated densely sampled version of the received SAR data. While experiments conducted with both synthetically generated and real airborne SAR data show that POLYPHASE retains comparable performance to the state-of-the-art BLUI scheme in image quality, a polyphase filter-based implementation of POLYPHASE offers significant computational savings for arbitrary (not necessarily periodic) input PRF variations, thus allowing fully on-board, in-place, and real-time implementation