Discrete multitone modulation with principal component filter banks

Discrete multitone (DMT) modulation is an attractive method for communication over a nonflat channel with possibly colored noise. The uniform discrete Fourier transform (DFT) filter bank and cosine modulated filter bank have in the past been used in this system because of low complexity. We show in this paper that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT modulation communication. For example, the PCFB of the effective channel noise power spectrum (noise psd weighted by the inverse of the channel gain) is optimal for DMT modulation in the sense of maximizing bit rate for fixed power and error probabilities. We also establish an optimality property of the PCFB when scalar prefilters and postfilters are used around the channel. The difference between the PCFB and a traditional filter bank such as the brickwall filter bank or DFT filter bank is significant for effective power spectra which depart considerably from monotonicity. The twisted pair channel with its bridged taps, next and fext noises, and AM interference, therefore appears to be a good candidate for the application of a PCFB. This is demonstrated with the help of numerical results for the case of the ADSL channel

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

Inversion of Parahermitian matrices

Parahermitian matrices arise in broadband multiple-input multiple-output (MIMO) systems or array processing, and require inversion in some instances. In this paper, we apply a polynomial eigenvalue decomposition obtained by the sequential best rotation algorithm to decompose a parahermitian matrix into a product of two paraunitary, i.e.lossless and easily invertible matrices, and a diagonal polynomial matrix. The inversion of the overall parahermitian matrix therefore reduces to the inversion of auto-correlation sequences in this diagonal matrix. We investigate a number of different approaches to obtain this inversion, and and assessment of the numerical stability and complexity of the inversion process

Efficiency in audio processing : filter banks and transcoding

Audio transcoding is the conversion of digital audio from one compressed form A to another compressed form B, where A and B have different compression properties, such as a different bit-rate, sampling frequency or compression method. This is typically achieved by decoding A to an intermediate uncompressed form, and then encoding it to B. A significant portion of the involved computational effort pertains to operating the synthesis filter bank, which is an important processing block in the decoding stage, and the analysis filter bank, which is an important processing block in the encoding stage. This thesis presents methods for efficient implementations of filter banks and audio transcoders, and is separated into two main parts. In the first part, a new class of Frequency Response Masking (FRM) filter banks is introduced. These filter banks are usually characterized by comprising a tree-structured cascade of subfilters, which have small individual filter lengths. Methods of complexity reduction are proposed for the scenarios when the filter banks are operated in single-rate mode, and when they are operated in multirate mode; and for the scenarios when the input signal is real-valued, and when it is complex-valued. An efficient variable bandwidth FRM filter bank is designed by using signed-powers-of-two reduction of its subfilter coefficients. Our design has a complexity an order lower than that of an octave filter bank with the same specifications. In the second part, the audio transcoding process is analyzed. Audio transcoding is modeled as a cascaded quantization process, and the cascaded quantization of an input signal is analyzed under different conditions, for the MPEG 1 Layer 2 and MP3 compression methods. One condition is the input-to-output delay of the transcoder, which is known to have an impact on the audio quality of the transcoded material. Methods to reduce the error in a cascaded quantization process are also proposed. An ultra-fast MP3 transcoder that requires only integer operations is proposed and implemented in software. Our implementation shows an improvement by a factor of 5 to 16 over other best known transcoders in terms of execution speed

Subspace-Based Blind Channel Identification for Cyclic Prefix Systems Using Few Received Blocks

In this paper, a novel generalization of subspace-based blind channel identification methods in cyclic prefix (CP) systems is proposed. For the generalization, a new system parameter called repetition index is introduced whose value is unity for previously reported special cases. By choosing a repetition index larger than unity, the number of received blocks needed for blind identification is significantly reduced compared to all previously reported methods. This feature makes the method more realistic especially in wireless environments where the channel state is usually fast-varying. Given the number of received blocks available, the minimum value of repetition index is derived. Theoretical limit allows the proposed method to perform blind identification using only three received blocks in absence of noise. In practice, the number of received blocks needed to yield a satisfactory bit-error-rate (BER) performance is usually on the order of half the block size. Simulation results not only demonstrate the capability of the algorithm to perform blind identification using fewer received blocks, but also show that in some cases system performance can be improved by choosing a repetition index larger than needed. Simulation of the proposed method over time-varying channels clearly demonstrates the improvement over previously reported methods

Lattice factorization and design of Perfect Reconstruction Filter Banks with any Length yielding linear phase

Publication in the conference proceedings of EUSIPCO, Florence, Italy, 200

On optimal design and applications of linear transforms

Linear transforms are encountered in many fields of applied science and engineering. In the past, conventional block transforms provided acceptable answers to different practical problems. But now, under increasing competitive pressures, with the growing reservoir of theory and a corresponding development of computing facilities, a real demand has been created for methods that systematically improve performance. As a result the past two decades have seen the explosive growth of a class of linear transform theory known as multiresolution signal decomposition. The goal of this work is to design and apply these advanced signal processing techniques to several different problems. The optimal design of subband filter banks is considered first. Several design examples are presented for M-band filter banks. Conventional design approaches are found to present problems when the number of constraints increases. A novel optimization method is proposed using a step-by-step design of a hierarchical subband tree. This method is shown to possess performance improvements in applications such as subband image coding. The subband tree structuring is then discussed and generalized algorithms are presented. Next, the attention is focused on the interference excision problem in direct sequence spread spectrum (DSSS) communications. The analytical and experimental performance of the DSSS receiver employing excision are presented. Different excision techniques are evaluated and ranked along with the proposed adaptive subband transform-based excises. The robustness of the considered methods is investigated for either time-localized or frequency-localized interferers. A domain switchable excision algorithm is also presented. Finally, sonic of the ideas associated with the interference excision problem are utilized in the spectral shaping of a particular biological signal, namely heart rate variability. The improvements for the spectral shaping process are shown for time-frequency analysis. In general, this dissertation demonstrates the proliferation of new tools for digital signal processing