Alias-free, real coefficient m-band QMF banks for arbitrary m

Based on a generalized framework for alias free QMF banks, a theory is developed for the design of uniform QMF banks with real-coefficient analysis filters, such that aliasing can be completely canceled by appropriate choice of real-coefficient synthesis filters. These results are then applied for the derivation of closed-form expressions for the synthesis filters (both FIR and IIR), that ensure cancelation of aliasing for a given set of analysis filters. The results do not involve the inversion of the alias-component (AC) matrix

Theory and design of uniform DFT, parallel, quadrature mirror filter banks

In this paper, the theory of uniform DFT, parallel, quadrature mirror filter (QMF) banks is developed. The QMF equations, i.e., equations that need to be satisfied for exact reconstruction of the input signal, are derived. The concept of decimated filters is introduced, and structures for both analysis and synthesis banks are derived using this concept. The QMF equations, as well as closed-form expressions for the synthesis filters needed for exact reconstruction of the input signalx(n), are also derived using this concept. In general, the reconstructed. signalhat{x}(n)suffers from three errors: aliasing, amplitude distortion, and phase distortion. Conditions for exact reconstruction (i.e., all three distortions are zero, andhat{x}(n)is equal to a delayed version ofx(n))of the input signal are derived in terms of the decimated filters. Aliasing distortion can always be completely canceled. Once aliasing is canceled, it is possible to completely eliminate amplitude distortion (if suitable IIR filters are employed) and completely eliminate phase distortion (if suitable FIR filters are employed). However, complete elimination of all three errors is possible only with some simple, pathalogical stable filter transfer functions. In general, once aliasing is canceled, the other distortions can be minimized rather than completely eliminated. Algorithms for this are presented. The properties of FIR filter banks are then investigated. Several aspects of IIR filter banks are also studied using the same framework

Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property

Based on the concept of losslessness in digital filter structures, this paper derives a general class of maximally decimated M-channel quadrature mirror filter banks that lead to perfect reconstruction. The perfect-reconstruction property guarantees that the reconstructed signalhat{x} (n)is a delayed version of the input signal x (n), i.e.,hat{x} (n) = x (n - n_{0}). It is shown that such a property can be satisfied if the alias component matrix (AC matrix for short) is unitary on the unit circle of the z plane. The number of channels M is arbitrary, and when M is two, the results reduce to certain recently reported 2-channel perfect-reconstruction QMF structures. A procedure, based on recently reported FIR cascaded-lattice structures, is presented for optimal design of such FIR M-channel filter banks. Design examples are included

Perfect reconstruction QMF banks for two-dimensional applications

A theory is outlined whereby it is possible to design a M x N channel two-dimensional quadrature mirror filter bank which has perfect reconstruction property. Such a property ensures freedom from aliasing, amplitude distortion, and phase distortion. The method is based on a simple property of certain transfer matrices, namely the losslessness property

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

The theory and design of a class of perfect reconstruction modified DFT filter banks with IIR filters

The 47th Midwest Symposium on Circuits and Systems Conference, Salt Lake City, Utah, USA, 25-28 July 2004This paper proposes a theory and design method for a class of PR causal-stable modified discrete Fourier transform (MDFT) filter bank (FB) with IIR filters. The prototype filter of the MDFT FB is assumed to have identical denominator in order to simplify the PR condition. A new model reduction technique is proposed for deriving a nearly PR (NPR) MDFT FB from a PR MDFT FB with FIR prototype filter. With these NPR IIR MDFT FBs as initial guess, PR IIR MDFT FBs with very good frequency characteristics can be obtained by solving a constrained nonlinear optimisation problem. Because the location of the poles can be approximately determined through model reduciton, the efficiency and reliability of the design method is significantly improved. Design examples are given to demonstrate the effectiveness of the proposed method.published_or_final_versio

Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial

Multirate digital filters and filter banks find application in communications, speech processing, image compression, antenna systems, analog voice privacy systems, and in the digital audio industry. During the last several years there has been substantial progress in multirate system research. This includes design of decimation and interpolation filters, analysis/synthesis filter banks (also called quadrature mirror filters, or QMFJ, and the development of new sampling theorems. First, the basic concepts and building blocks in multirate digital signal processing (DSPJ, including the digital polyphase representation, are reviewed. Next, recent progress as reported by several authors in this area is discussed. Several applications are described, including the following: subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrow-band filter coefficients. The M-band QMF bank is discussed in considerable detail, including an analysis of various errors and imperfections. Recent techniques for perfect signal reconstruction in such systems are reviewed. The connection between QMF banks and other related topics, such as block digital filtering and periodically time-varying systems, based on a pseudo-circulant matrix framework, is covered. Unconventional applications of the polyphase concept are discussed

Polyphase networks, block digital filtering, LPTV systems, and alias-free QMF banks: a unified approach based on pseudocirculants

The relationship between block digital filtering and quadrature mirror filter (QMF) banks is explored. Necessary and sufficient conditions for alias cancellation in QMF banks are expressed in terms of an associated matrix, derived from the polyphase components of the analysis and synthesis filters. These conditions, called the pseudocirculant conditions, make it possible to unite QMF banks with the framework of block digital filtering directly. Absence of amplitude distortion in an alias-free QMF bank translates into the 'losslessness' property of the pseudocirculant matrix involved

Filter Bank Multicarrier Modulation for Spectrally Agile Waveform Design

In recent years the demand for spectrum has been steadily growing. With the limited amount of spectrum available, Spectrum Pooling has gained immense popularity. As a result of various studies, it has been established that most of the licensed spectrum remains underutilized. Spectrum Pooling or spectrum sharing concentrates on making the most of these whitespaces in the licensed spectrum. These unused parts of the spectrum are usually available in chunks. A secondary user looking to utilize these chunks needs a device capable of transmitting over distributed frequencies, while not interfering with the primary user. Such a process is known as Dynamic Spectrum Access (DSA) and a device capable of it is known as Cognitive Radio. In such a scenario, multicarrier communication that transmits data across the channel in several frequency subcarriers at a lower data rate has gained prominence. Its appeal lies in the fact that it combats frequency selective fading. Two methods for implementing multicarrier modulation are non-contiguous orthogonal frequency division multiplexing (NCOFDM)and filter bank multicarrier modulation (FBMC). This thesis aims to implement a novel FBMC transmitter using software defined radio (SDR) with modulated filters based on a lowpass prototype. FBMCs employ two sets of bandpass filters called analysis and synthesis filters, one at the transmitter and the other at the receiver, in order to filter the collection of subcarriers being transmitted simultaneously in parallel frequencies. The novel aspect of this research is that a wireless transmitter based on non-contiguous FBMC is being used to design spectrally agile waveforms for dynamic spectrum access as opposed to the more popular NC-OFDM. Better spectral containment and bandwidth efficiency, combined with lack of cyclic prefix processing, makes it a viable alternative for NC-OFDM. The main aim of this thesis is to prove that FBMC can be practically implemented for wireless communications. The practicality of the method is tested by transmitting the FBMC signals real time by using the Simulink environment and USRP2 hardware modules