Broadband adaptive beamforming with low complexity and frequency invariant response

This thesis proposes different methods to reduce the computational complexity as well as increasing the adaptation rate of adaptive broadband beamformers. This is performed exemplarily for the generalised sidelobe canceller (GSC) structure. The GSC is an alternative implementation of the linearly constrained minimum variance beamformer, which can utilise well-known adaptive filtering algorithms, such as the least mean square (LMS) or the recursive least squares (RLS) to perform unconstrained adaptive optimisation.A direct DFT implementation, by which broadband signals are decomposed into frequency bins and processed by independent narrowband beamforming algorithms, is thought to be computationally optimum. However, this setup fail to converge to the time domain minimum mean square error (MMSE) if signal components are not aligned to frequency bins, resulting in a large worst case error. To mitigate this problem of the so-called independent frequency bin (IFB) processor, overlap-save based GSC beamforming structures have been explored. This system address the minimisation of the time domain MMSE, with a significant reduction in computational complexity when compared to time-domain implementations, and show a better convergence behaviour than the IFB beamformer. By studying the effects that the blocking matrix has on the adaptive process for the overlap-save beamformer, several modifications are carried out to enhance both the simplicity of the algorithm as well as its convergence speed. These modifications result in the GSC beamformer utilising a significantly lower computational complexity compare to the time domain approach while offering similar convergence characteristics.In certain applications, especially in the areas of acoustics, there is a need to maintain constant resolution across a wide operating spectrum that may extend across several octaves. To attain constant beamwidth is difficult, particularly if uniformly spaced linear sensor array are employed for beamforming, since spatial resolution is reciprocally proportional to both the array aperture and the frequency. A scaled aperture arrangement is introduced for the subband based GSC beamformer to achieve near uniform resolution across a wide spectrum, whereby an octave-invariant design is achieved. This structure can also be operated in conjunction with adaptive beamforming algorithms. Frequency dependent tapering of the sensor signals is proposed in combination with the overlap-save GSC structure in order to achieve an overall frequency-invariant characteristic. An adaptive version is proposed for frequency-invariant overlap-save GSC beamformer. Broadband adaptive beamforming algorithms based on the family of least mean squares (LMS) algorithms are known to exhibit slow convergence if the input signal is correlated. To improve the convergence of the GSC when based on LMS-type algorithms, we propose the use of a broadband eigenvalue decomposition (BEVD) to decorrelate the input of the adaptive algorithm in the spatial dimension, for which an increase in convergence speed can be demonstrated over other decorrelating measures, such as the Karhunen-Loeve transform. In order to address the remaining temporal correlation after BEVD processing, this approach is combined with subband decomposition through the use of oversampled filter banks. The resulting spatially and temporally decorrelated GSC beamformer provides further enhanced convergence speed over spatial or temporal decorrelation methods on their own

Unified Theory for Biorthogonal Modulated Filter Banks

Modulated filter banks (MFBs) are practical signal decomposition tools for M -channel multirate systems. They combine high subfilter selectivity with efficient realization based on polyphase filters and block transforms. Consequently, the O(M 2 ) burden of computations in a general filter bank (FB) is reduced to O(M log2 M ) - the latter being a complexity order comparable with the FFT-like transforms.Often hiding from the plain sight, these versatile digital signal processing tools have important role in various professional and everyday life applications of information and communications technology, including audiovisual communications and media storage (e.g., audio codecs for low-energy music playback in portable devices, as well as communication waveform processing and channelization). The algorithmic efficiency implies low cost, small size, and extended battery life, bringing the devices close to our skins.The main objective of this thesis is to formulate a generalized and unified approach to the MFBs, which includes, in addition to the deep theoretical background behind these banks, both their design by using appropriate optimization techniques and efficient algorithmic realizations. The FBs discussed in this thesis are discrete-time time-frequency decomposition/reconstruction, or equivalently, analysis-synthesis systems, where the subfilters are generated through modulation from either a single or two prototype filters. The perfect reconstruction (PR) property is a particularly important characteristics of the MFBs and this is the core theme of this thesis. In the presented biorthogonal arbitrary-delay exponentially modulated filter bank (EMFB), the PR property can be maintained also for complex-valued signals.The EMFB concept is quite flexible, since it may respond to the various requirements given to a subband processing system: low-delay PR prototype design, subfilters having symmetric impulse responses, efficient algorithms, and the definition covers odd and even-stacked cosine-modulated FBs as special cases. Oversampling schemes for the subsignals prove out to be advantageous in subband processing problems requiring phase information about the localized frequency components. In addition, the MFBs have strong connections with the lapped transform (LT) theory, especially with the class of LTs grounded in parametric window functions.<br/

Algorithms and architectures for the multirate additive synthesis of musical tones

In classical Additive Synthesis (AS), the output signal is the sum of a large number of independently controllable sinusoidal partials. The advantages of AS for music synthesis are well known as is the high computational cost. This thesis is concerned with the computational optimisation of AS by multirate DSP techniques. In note-based music synthesis, the expected bounds of the frequency trajectory of each partial in a finite lifecycle tone determine critical time-invariant partial-specific sample rates which are lower than the conventional rate (in excess of 40kHz) resulting in computational savings. Scheduling and interpolation (to suppress quantisation noise) for many sample rates is required, leading to the concept of Multirate Additive Synthesis (MAS) where these overheads are minimised by synthesis filterbanks which quantise the set of available sample rates. Alternative AS optimisations are also appraised. It is shown that a hierarchical interpretation of the QMF filterbank preserves AS generality and permits efficient context-specific adaptation of computation to required note dynamics. Practical QMF implementation and the modifications necessary for MAS are discussed. QMF transition widths can be logically excluded from the MAS paradigm, at a cost. Therefore a novel filterbank is evaluated where transition widths are physically excluded. Benchmarking of a hypothetical orchestral synthesis application provides a tentative quantitative analysis of the performance improvement of MAS over AS. The mapping of MAS into VLSI is opened by a review of sine computation techniques. Then the functional specification and high-level design of a conceptual MAS Coprocessor (MASC) is developed which functions with high autonomy in a loosely-coupled master- slave configuration with a Host CPU which executes filterbanks in software. Standard hardware optimisation techniques are used, such as pipelining, based upon the principle of an application-specific memory hierarchy which maximises MASC throughput

Multiresolution techniques for audio signal restoration

This thesis describes a study of techniques for the restoration of musical audio signals using a multiresolution signal representation called the multiresolution Fourier transform (MFT), a time-frequency-scale representation. This representation allows the restoration to adapt to the local signal structure, which typically consists of a set of approximately sinusoidal partials, each consisting of an “onset” of rapid energy variation followed by more slowly varying “sustain” and “decay” phases. It must be decided what components of a noisy audio signal are to be kept in the restored version and, conversely, which must be removed. A simple filter is introduced that retains only musical signal —that is signal which adheres to the musical model — and rejects everything else. It is shown that this filter used in conjunction with the MIT has a low computational complexity. The MIT is used to capture the transient energy present at the onset of notes by splitting the time axis of a musical signal into steady-state and transient zones using a simple onset detector, which measures the expected energy at a given lime against the actual energy present. Past audio signal restoration systems have relied on estimating a restored audio signal’s spectrum from the noisy audio signal presented to the algorithm. In this thesis the idea of having more than one version of a recording is used in order to gain further information about the ideal spectrum of the noisy signal. This poses a number of problems with regards to matching the time scales of two versions of the same piece. These are addressed and solutions are offered, based on a novel multiresolution warping algorithm. Finally, various methods for using the detected signal spectrum of a clean modern signal to restore a noisy signal using the warping techniques and musical event detection filters are shown. These account for variations in scale and input signal to noise ratio (SNR) in the noisy signal. It is also shown how the simple adaptive filter introduced earlier can be used to restore audio signals with impulse noise as well as while additive noise. This filter and the time-warping technique is compared to adaptive Wiener filtering as an audio restoration method

Adaptive spatial combining for passive time-reversed communications

Passive time reversal has aroused considerable interest in underwater communications as a computationally inexpensive means of mitigating the intersymbol interference introduced by the channel using a receiver array. In this paper the basic technique is extended by adaptively weighting sensor contributions to partially compensate for degraded focusing due to mismatch between the assumed and actual medium impulse responses. Two algorithms are proposed, one of which restores constructive interference between sensors, and the other one minimizes the output residual as in widely used equalization schemes. These are compared with plain time reversal and variants that employ postequalization and channel tracking. They are shown to improve the residual error and temporal stability of basic time reversal with very little added complexity. Results are presented for data collected in a passive time-reversal experiment that was conducted during the MREA’04 sea trial. In that experiment a single acoustic projector generated a 2/4-PSK phase-shift keyed stream at 200/400 baud, modulated at 3.6 kHz, and received at a range of about 2 km on a sparse vertical array with eight hydrophones. The data were found to exhibit significant Doppler scaling, and a resampling-based preprocessing method is also proposed here to compensate for that scaling