A 'trick' for the design of FIR half-band filters

Based on a well-known property of FIR half-band filters, this correspondence shows how the design time for equiripple half-band filters can be reduced by a considerable amount. The observation which leads up to this improved procedure also places in evidence new implementation schemes, which simultaneously ensure low passband and stopband sensitivities. Extension of the method to Mth-band filter design is also outlined

Efficient reconstruction of band-limited sequences from nonuniformly decimated versions by use of polyphase filter banks

An efficient polyphase structure for the reconstruction of a band-limited sequence from a nonuniformly decimated version is developed. Theoretically, the reconstruction involves the implementation of a bank of multilevel filters, and it is shown that how all these reconstruction filters can be obtained at the cost of one Mth band low-pass filter and a constant matrix multiplier. The resulting structure is therefore more general than previous schemes. In addition, the method offers a direct means of controlling the overall reconstruction distortion T(z) by appropriate design of a low-pass prototype filter P(z). Extension of these results to multiband band-limited signals and to the case of nonconsecutive nonuniform subsampling are also summarized, along with generalizations to the multidimensional case. Design examples are included to demonstrate the theory, and the complexity of the new method is seen to be much lower than earlier ones

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

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

Efficient Algorithms for Immersive Audio Rendering Enhancement

Il rendering audio immersivo è il processo di creazione di un’esperienza sonora coinvolgente e realistica nello spazio 3D. Nei sistemi audio immersivi, le funzioni di trasferimento relative alla testa (head-related transfer functions, HRTFs) vengono utilizzate per la sintesi binaurale in cuffia poiché esprimono il modo in cui gli esseri umani localizzano una sorgente sonora. Possono essere introdotti algoritmi di interpolazione delle HRTF per ridurre il numero di punti di misura e per creare un movimento del suono affidabile. La riproduzione binaurale può essere eseguita anche dagli altoparlanti. Tuttavia, il coinvolgimento di due o più gli altoparlanti causa il problema del crosstalk. In questo caso, algoritmi di cancellazione del crosstalk (CTC) sono necessari per eliminare i segnali di interferenza indesiderati. In questa tesi, partendo da un'analisi comparativa di metodi di misura delle HRTF, viene proposto un sistema di rendering binaurale basato sull'interpolazione delle HRTF per applicazioni in tempo reale. Il metodo proposto mostra buone prestazioni rispetto a una tecnica di riferimento. L'algoritmo di interpolazione è anche applicato al rendering audio immersivo tramite altoparlanti, aggiungendo un algoritmo di cancellazione del crosstalk fisso, che considera l'ascoltatore in una posizione fissa. Inoltre, un sistema di cancellazione crosstalk adattivo, che include il tracciamento della testa dell'ascoltatore, è analizzato e implementato in tempo reale. Il CTC adattivo implementa una struttura in sottobande e risultati sperimentali dimostrano che un maggiore numero di bande migliora le prestazioni in termini di errore totale e tasso di convergenza. Il sistema di riproduzione e le caratteristiche dell'ambiente di ascolto possono influenzare le prestazioni a causa della loro risposta in frequenza non ideale. L'equalizzazione viene utilizzata per livellare le varie parti dello spettro di frequenze che compongono un segnale audio al fine di ottenere le caratteristiche sonore desiderate. L'equalizzazione può essere manuale, come nel caso dell'equalizzazione grafica, dove il guadagno di ogni banda di frequenza può essere modificato dall'utente, o automatica, la curva di equalizzazione è calcolata automaticamente dopo la misurazione della risposta impulsiva della stanza. L'equalizzazione della risposta ambientale può essere applicata anche ai sistemi multicanale, che utilizzano due o più altoparlanti e la zona di equalizzazione può essere ampliata misurando le risposte impulsive in diversi punti della zona di ascolto. In questa tesi, GEQ efficienti e un sistema adattativo di equalizzazione d'ambiente. In particolare, sono proposti e approfonditi tre equalizzatori grafici a basso costo computazionale e a fase lineare e quasi lineare. Gli esperimenti confermano l'efficacia degli equalizzatori proposti in termini di accuratezza, complessità computazionale e latenza. Successivamente, una struttura adattativa in sottobande è introdotta per lo sviluppo di un sistema di equalizzazione d'ambiente multicanale. I risultati sperimentali verificano l'efficienza dell'approccio in sottobande rispetto al caso a banda singola. Infine, viene presentata una rete crossover a fase lineare per sistemi multicanale, mostrando ottimi risultati in termini di risposta in ampiezza, bande di transizione, risposta polare e risposta in fase. I sistemi di controllo attivo del rumore (ANC) possono essere progettati per ridurre gli effetti dell'inquinamento acustico e possono essere utilizzati contemporaneamente a un sistema audio immersivo. L'ANC funziona creando un'onda sonora in opposizione di fase rispetto all'onda sonora in arrivo. Il livello sonoro complessivo viene così ridotto grazie all'interferenza distruttiva. Infine, questa tesi presenta un sistema ANC utilizzato per la riduzione del rumore. L’approccio proposto implementa una stima online del percorso secondario e si basa su filtri adattativi in sottobande applicati alla stima del percorso primario che mirano a migliorare le prestazioni dell’intero sistema. La struttura proposta garantisce un tasso di convergenza migliore rispetto all'algoritmo di riferimento.Immersive audio rendering is the process of creating an engaging and realistic sound experience in 3D space. In immersive audio systems, the head-related transfer functions (HRTFs) are used for binaural synthesis over headphones since they express how humans localize a sound source. HRTF interpolation algorithms can be introduced for reducing the number of measurement points and creating a reliable sound movement. Binaural reproduction can be also performed by loudspeakers. However, the involvement of two or more loudspeakers causes the problem of crosstalk. In this case, crosstalk cancellation (CTC) algorithms are needed to delete unwanted interference signals. In this thesis, starting from a comparative analysis of HRTF measurement techniques, a binaural rendering system based on HRTF interpolation is proposed and evaluated for real-time applications. The proposed method shows good performance in comparison with a reference technique. The interpolation algorithm is also applied for immersive audio rendering over loudspeakers, by adding a fixed crosstalk cancellation algorithm, which assumes that the listener is in a fixed position. In addition, an adaptive crosstalk cancellation system, which includes the tracking of the listener's head, is analyzed and a real-time implementation is presented. The adaptive CTC implements a subband structure and experimental results prove that a higher number of bands improves the performance in terms of total error and convergence rate. The reproduction system and the characteristics of the listening room may affect the performance due to their non-ideal frequency response. Audio equalization is used to adjust the balance of different audio frequencies in order to achieve desired sound characteristics. The equalization can be manual, such as in the case of graphic equalization, where the gain of each frequency band can be modified by the user, or automatic, where the equalization curve is automatically calculated after the room impulse response measurement. The room response equalization can be also applied to multichannel systems, which employ two or more loudspeakers, and the equalization zone can be enlarged by measuring the impulse responses in different points of the listening zone. In this thesis, efficient graphic equalizers (GEQs), and an adaptive room response equalization system are presented. In particular, three low-complexity linear- and quasi-linear-phase graphic equalizers are proposed and deeply examined. Experiments confirm the effectiveness of the proposed GEQs in terms of accuracy, computational complexity, and latency. Successively, a subband adaptive structure is introduced for the development of a multichannel and multiple positions room response equalizer. Experimental results verify the effectiveness of the subband approach in comparison with the single-band case. Finally, a linear-phase crossover network is presented for multichannel systems, showing great results in terms of magnitude flatness, cutoff rates, polar diagram, and phase response. Active noise control (ANC) systems can be designed to reduce the effects of noise pollution and can be used simultaneously with an immersive audio system. The ANC works by creating a sound wave that has an opposite phase with respect to the sound wave of the unwanted noise. The additional sound wave creates destructive interference, which reduces the overall sound level. Finally, this thesis presents an ANC system used for noise reduction. The proposed approach implements an online secondary path estimation and is based on cross-update adaptive filters applied to the primary path estimation that aim at improving the performance of the whole system. The proposed structure allows for a better convergence rate in comparison with a reference algorithm

Passive cascaded-lattice structures for low-sensitivity FIR filter design, with applications to filter banks

A class of nonrecursive cascaded-lattice structures is derived, for the implementation of finite-impulse response (FIR) digital filters. The building blocks are lossless and the transfer function can be implemented as a sequence of planar rotations. The structures can be used for the synthesis of any scalar FIR transfer function H(z) with no restriction on the location of zeros; at the same time, all the lattice coefficients have magnitude bounded above by unity. The structures have excellent passband sensitivity because of inherent passivity, and are automatically internally scaled, in an L_2 sense. The ideas are also extended for the realization of a bank of MFIR transfer functions as a cascaded lattice. Applications of these structures in subband coding and in multirate signal processing are outlined. Numerical design examples are included

Design of FIR digital filters for pulse shaping and channel equalization using time-domain optimization

Three algorithms are developed for designing finite impulse response digital filters to be used for pulse shaping and channel equalization. The first is the Minimax algorithm which uses linear programming to design a frequency-sampling filter with a pulse shape that approximates the specification in a minimax sense. Design examples are included which accurately approximate a specified impulse response with a maximum error of 0.03 using only six resonators. The second algorithm is an extension of the Minimax algorithm to design preset equalizers for channels with known impulse responses. Both transversal and frequency-sampling equalizer structures are designed to produce a minimax approximation of a specified channel output waveform. Examples of these designs are compared as to the accuracy of the approximation, the resultant intersymbol interference (ISI), and the required transmitted energy. While the transversal designs are slightly more accurate, the frequency-sampling designs using six resonators have smaller ISI and energy values

System Identification with Applications in Speech Enhancement

As the increasing popularity of integrating hands-free telephony on mobile portable devices and the rapid development of voice over internet protocol, identification of acoustic systems has become desirable for compensating distortions introduced to speech signals during transmission, and hence enhancing the speech quality. The objective of this research is to develop system identification algorithms for speech enhancement applications including network echo cancellation and speech dereverberation. A supervised adaptive algorithm for sparse system identification is developed for network echo cancellation. Based on the framework of selective-tap updating scheme on the normalized least mean squares algorithm, the MMax and sparse partial update tap-selection strategies are exploited in the frequency domain to achieve fast convergence performance with low computational complexity. Through demonstrating how the sparseness of the network impulse response varies in the transformed domain, the multidelay filtering structure is incorporated to reduce the algorithmic delay. Blind identification of SIMO acoustic systems for speech dereverberation in the presence of common zeros is then investigated. First, the problem of common zeros is defined and extended to include the presence of near-common zeros. Two clustering algorithms are developed to quantify the number of these zeros so as to facilitate the study of their effect on blind system identification and speech dereverberation. To mitigate such effect, two algorithms are developed where the two-stage algorithm based on channel decomposition identifies common and non-common zeros sequentially; and the forced spectral diversity approach combines spectral shaping filters and channel undermodelling for deriving a modified system that leads to an improved dereverberation performance. Additionally, a solution to the scale factor ambiguity problem in subband-based blind system identification is developed, which motivates further research on subbandbased dereverberation techniques. Comprehensive simulations and discussions demonstrate the effectiveness of the aforementioned algorithms. A discussion on possible directions of prospective research on system identification techniques concludes this thesis

Optimization design of mth-band FIR filters with application to image processing

Cone programming (CP) is a class of convex optimization technique, in which a linear objective function is minimized over the intersection of a set of affine constraints. Such constraints could be linear or convex, equalities or inequalities. Owing to its powerful optimization capability as well as flexibility in accommodating various constraints, the cone programming finds wide applications in digital filter design. In this thesis, fundamentals of linear-phase M th-band FIR filters are first introduced, which include the time-domain interpolation condition and the desired frequency specifications. The restriction of the interpolation matrix M for linear-phase two-dimensional (2-D) M th-band filters is also discussed by considering both the interpolation condition and the symmetry of the impulse response of the 2-D filter. Based on the analysis of the M th-band properties, a semidefinite programming (SOP) optimization approach is developed to design linear-phase 1-0 and 2-D M th-band filters. The 2-D SOP optimization design problem is modeled based on both the mini-max and the least-square error criteria. In contrast to the 1-D based design, the 2-D direct SDP design can offer an optimal equiripple result. A second-order cone programming (SOCP) optimization approach is then presented as an alternative for the design of M th-band filters. The performances as well as the design complexity of these two design approaches are justified through numerical design examples. Simulation results show that the performance of the SOCP approach is better than that of the SDP approach for 1-D M th-band filter design due to its reduced computational complexity for the worst-case, whereas the SDP approach is more appropriate for the 2-D M th-band filter design than the SOCP approach because of its efficient and simple optimization structure. Moreover, the designed M th-band filters are proved useful in image interpolation according to both the visual quality and the peak signal-to-noise ratio (PSNR) for the images with different levels of details