One- and two-level filter-bank convolvers

In a recent paper, it was shown in detail that in the case of orthonormal and biorthogonal filter banks we can convolve two signals by directly convolving the subband signals and combining the results. In this paper, we further generalize the result. We also derive the statistical coding gain for the generalized subband convolver. As an application, we derive a novel low sensitivity structure for FIR filters from the convolution theorem. We define and derive a deterministic coding gain of the subband convolver over direct convolution for a fixed wordlength implementation. This gain serves as a figure of merit for the low sensitivity structure. Several numerical examples are included to demonstrate the usefulness of these ideas. By using the generalized polyphase representation, we show that the subband convolvers, linear periodically time varying systems, and digital block filtering can be viewed in a unified manner. Furthermore, the scheme called IFIR filtering is shown to be a special case of the convolver

Doctor of Philosophy

dissertationHearing aids suffer from the problem of acoustic feedback that limits the gain provided by hearing aids. Moreover, the output sound quality of hearing aids may be compromised in the presence of background acoustic noise. Digital hearing aids use advanced signal processing to reduce acoustic feedback and background noise to improve the output sound quality. However, it is known that the output sound quality of digital hearing aids deteriorates as the hearing aid gain is increased. Furthermore, popular subband or transform domain digital signal processing in modern hearing aids introduces analysis-synthesis delays in the forward path. Long forward-path delays are not desirable because the processed sound combines with the unprocessed sound that arrives at the cochlea through the vent and changes the sound quality. In this dissertation, we employ a variable, frequency-dependent gain function that is lower at frequencies of the incoming signal where the information is perceptually insignificant. In addition, the method of this dissertation automatically identifies and suppresses residual acoustical feedback components at frequencies that have the potential to drive the system to instability. The suppressed frequency components are monitored and the suppression is removed when such frequencies no longer pose a threat to drive the hearing aid system into instability. Together, the method of this dissertation provides more stable gain over traditional methods by reducing acoustical coupling between the microphone and the loudspeaker of a hearing aid. In addition, the method of this dissertation performs necessary hearing aid signal processing with low-delay characteristics. The central idea for the low-delay hearing aid signal processing is a spectral gain shaping method (SGSM) that employs parallel parametric equalization (EQ) filters. Parameters of the parametric EQ filters and associated gain values are selected using a least-squares approach to obtain the desired spectral response. Finally, the method of this dissertation switches to a least-squares adaptation scheme with linear complexity at the onset of howling. The method adapts to the altered feedback path quickly and allows the patient to not lose perceivable information. The complexity of the least-squares estimate is reduced by reformulating the least-squares estimate into a Toeplitz system and solving it with a direct Toeplitz solver. The increase in stable gain over traditional methods and the output sound quality were evaluated with psychoacoustic experiments on normal-hearing listeners with speech and music signals. The results indicate that the method of this dissertation provides 8 to 12 dB more hearing aid gain than feedback cancelers with traditional fixed gain functions. Furthermore, experimental results obtained with real world hearing aid gain profiles indicate that the method of this dissertation provides less distortion in the output sound quality than classical feedback cancelers, enabling the use of more comfortable style hearing aids for patients with moderate to profound hearing loss. Extensive MATLAB simulations and subjective evaluations of the results indicate that the method of this dissertation exhibits much smaller forward-path delays with superior howling suppression capability

Residual echo signal in critically sampled subband acoustic echo cancellers based on IIR and FIR filter banks

Published 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

Theory and design of a class of cosine-modulated non-uniform filter banks

In this paper, the theory and design of a class of PR cosine-modulated nonuniform filter bank is proposed. It is based on a structure previously proposed by Cox, where the outputs of a uniform filter bank is combined or merged by means of the synthesis section of another filter bank with smaller channel number. Simplifications are imposed on this structure so that the design procedure can be considerably simplified. Due to the use of CMFB as the original and recombination filter banks, excellent filter quality and low design and implementation complexities can be achieved. Problems with these merging techniques such as spectrum inversion, equivalent filter representations and protrusion cancellation are also addressed. As the merging is performed after the decimation, the arithmetic complexity is lower than other conventional approaches. Design examples show that PR nonuniform filter banks with high stopband attenuation and low design and implementation complexities can be obtained by the proposed method.published_or_final_versio

A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data

New Directions in Subband Coding

Two very different subband coders are described. The first is a modified dynamic bit-allocation-subband coder (D-SBC) designed for variable rate coding situations and easily adaptable to noisy channel environments. It can operate at rates as low as 12 kb/s and still give good quality speech. The second coder is a 16-kb/s waveform coder, based on a combination of subband coding and vector quantization (VQ-SBC). The key feature of this coder is its short coding delay, which makes it suitable for real-time communication networks. The speech quality of both coders has been enhanced by adaptive postfiltering. The coders have been implemented on a single AT&T DSP32 signal processo

Efficient Multiband Algorithms for Blind Source Separation

The problem of blind separation refers to recovering original signals, called source signals, from the mixed signals, called observation signals, in a reverberant environment. The mixture is a function of a sequence of original speech signals mixed in a reverberant room. The objective is to separate mixed signals to obtain the original signals without degradation and without prior information of the features of the sources. The strategy used to achieve this objective is to use multiple bands that work at a lower rate, have less computational cost and a quicker convergence than the conventional scheme. Our motivation is the competitive results of unequal-passbands scheme applications, in terms of the convergence speed. The objective of this research is to improve unequal-passbands schemes by improving the speed of convergence and reducing the computational cost. The first proposed work is a novel maximally decimated unequal-passbands scheme.This scheme uses multiple bands that make it work at a reduced sampling rate, and low computational cost. An adaptation approach is derived with an adaptation step that improved the convergence speed. The performance of the proposed scheme was measured in different ways. First, the mean square errors of various bands are measured and the results are compared to a maximally decimated equal-passbands scheme, which is currently the best performing method. The results show that the proposed scheme has a faster convergence rate than the maximally decimated equal-passbands scheme. Second, when the scheme is tested for white and coloured inputs using a low number of bands, it does not yield good results; but when the number of bands is increased, the speed of convergence is enhanced. Third, the scheme is tested for quick changes. It is shown that the performance of the proposed scheme is similar to that of the equal-passbands scheme. Fourth, the scheme is also tested in a stationary state. The experimental results confirm the theoretical work. For more challenging scenarios, an unequal-passbands scheme with over-sampled decimation is proposed; the greater number of bands, the more efficient the separation. The results are compared to the currently best performing method. Second, an experimental comparison is made between the proposed multiband scheme and the conventional scheme. The results show that the convergence speed and the signal-to-interference ratio of the proposed scheme are higher than that of the conventional scheme, and the computation cost is lower than that of the conventional scheme