Digital filter design using root moments for sum-of-all-pass structures from complete and partial specifications

Published versio

Minimal structures for the implementation of digital rational lossless systems

Digital lossless transfer matrices and vectors (power-complementary vectors) are discussed for applications in digital filter bank systems, both single rate and multirate. Two structures for the implementation of rational lossless systems are presented. The first structure represents a characterization of single-input, multioutput lossless systems in terms of complex planar rotations, whereas the second structure offers a representation of M-input, M-output lossless systems in terms of unit-norm vectors. This property makes the second structure desirable in applications that involve optimization of the parameters. Modifications of the second structure for implementing single-input, multioutput, and lossless bounded real (LBR) systems are also included. The main importance of the structures is that they are completely general, i.e. they span the entire set of M×1 and M×M lossless systems. This is demonstrated by showing that any such system can be synthesized using these structures. The structures are also minimal in the sense that they use the smallest number of scalar delays and parameters to implement a lossless system of given degree and dimensions. A design example to demonstrate the main results is included

The discrete-time bounded-real lemma in digital filtering

The Lossless Bounded-Real lemma is developed in the discrete-time domain, based only on energy balance arguments. The results are used to prove a discrete-time version of the general Bounded-Real lemma, based on a matrix spectral-factorization result that permits a transfer matrix embedding process. Some applications of the results in digital filter theory are finally outlined

Equalization with oversampling in multiuser CDMA systems

Some of the major challenges in the design of new-generation wireless mobile systems are the suppression of multiuser interference (MUI) and inter-symbol interference (ISI) within a single user created by the multipath propagation. Both of these problems were addressed successfully in a recent design of A Mutually Orthogonal Usercode-Receiver (AMOUR) for asynchronous or quasisynchronous code division multiple access (CDMA) systems. AMOUR converts a multiuser CDMA system into parallel single-user systems regardless of the multipath and guarantees ISI mitigation, irrespective of the channel locations. However, the noise amplification at the receiver can be significant in some multipath channels. In this paper, we propose to oversample the received signal as a way of improving the performance of AMOUR systems. We design Fractionally Spaced AMOUR (FSAMOUR) receivers with integral and rational amounts of oversampling and compare their performance with the conventional method. An important point that is often overlooked in the design of zero-forcing channel equalizers is that sometimes, they are not unique. This becomes especially significant in multiuser applications where, as we will show, the nonuniqueness is practically guaranteed. We exploit this flexibility in the design of AMOUR and FSAMOUR receivers and achieve noticeable improvements in performance

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