Michael Goodwin

Matching pursuit and atomic signal models based on recursive filter banks

Time-frequency atomic models are useful for signal analysis, modification, and coding, especially when the time-frequency behavior of the atoms matches the behavior of the signal. Such adaptive representations can be derived using the matching pursuit algorithm with an overcomplete dictionary of time-frequency atoms. In this paper, we consider matching pursuit with atoms constructed by coupling causal and anticausal damped sinusoids. These provide advantages over symmetric Gabor atoms for modeling signals with transient behavior, such as music. Furthermore, the matching pursuit computation is simplified by the structure of the atoms; expansions based on these atoms can be derived using simple recursive filter banks.

Matching pursuit with damped sinusoids

The matching pursuit algorithm derives an expansion of a signal in terms of the elements of a large dictionary of time-frequency atoms. This paper considers the use of matching pursuit for computing signal expansions in terms of damped sinusoids. First, expansion based on complex damped sinusoids is explored; it is shown that the expansion can be efficiently derived using the FFT and simple recursive filterbanks. Then, the approach is extended to provide decompositions in terms of real damped sinusoids. This extension relies on generalizing the matching pursuit algorithm to derive expansions with respect to dictionary subspaces; of specific interest is the subspace spanned by a complex atom and its conjugate. Developing this particular case leads to a framework for deriving real-valued expansions of real signals using complex atoms. Applications of the damped sinusoidal decomposition include system identification, spectral estimation, and signal modeling for coding and analysis-modification-synthesis.

Optimal time segmentation for signal modeling and compression

The idea of optimal joint time segmentation and resource allocation for signal modeling is explored with respect to arbitrary segmentations and arbitrary representation schemes. When the chosen signal modeling techniques can be quantified in terms of a cost function which is additive over distinct segments, a dynamic programming approach guarantees the global optimality of the scheme while keeping the computational requirements of the algorithm sufficiently low. Two immediate applications of the algorithm to LPC speech coding and to sinusoidal modeling of musical signals are presented.

Time-frequency signal models for music analysis, transformation, and synthesis

In signal analysis-synthesis, the analysis derives a set of parameters that the synthesis uses to reconstruct the original signal. In musical applications, this reconstruction should be perceptually accurate, and the parameterization should allow for such desirable signal modifications as time-scaling, pitch-shifting and cross-synthesis; the analysis parameters should correspond to a signal model that is flexible enough to allow these transformations. Sinusoidal modeling meets this flexibility requirement, but has difficulty representing some salient features of musical signals such as attack transients and noise-like processes. Sinusoidal modeling is reviewed and some variations are proposed to account for its shortcomings; also, wavelet-based representations of musical signals are considered.

Multiresolution sinusoidal modeling using adaptive segmentation

The sinusoidal model has proven useful for representation and modification of speech and audio. One drawback, however, is that a sinusoidal signal model is typically derived using a fixed frame size, which corresponds to a rigid signal segmentation. For nonstationary signals, the resolution limitations that result from this rigidity lead to reconstruction artifacts. It is shown in this paper that such artifacts can be significantly reduced by using a signal-adaptive segmentation derived by a dynamic program. An atomic interpretation of the sinusoidal model is given; this perspective suggests that algorithms for adaptive segmentation can be viewed as methods for adapting the time scales of the constituent atoms so as to improve the model by employing appropriate time-frequency tradeoffs.

Atomic decompositions of audio signals

Signal modeling techniques ranging from basis expansions to parametric approaches have been applied to audio signal processing. Motivated by the fundamental limitations of basis expansions for representing arbitrary signal features and providing means for signal modifications, we consider decompositions in terms of functions that are both signal-adaptive and parametric in nature. Granular synthesis and sinusoidal modeling can be viewed in this light; we interpret these approaches as signal-adaptive expansions in terms of time-frequency atoms that are highly correlated to the fundamental signal structures. This leads naturally to a discussion of the matching pursuit algorithm for deriving decompositions using over complete dictionaries of time-frequency atoms; specifically, we compare expansions using Gabor atoms and damped sinusoids. Such decompositions identify important signal features and provide parametric representations that are useful for signal coding and analysis-modification-synthesis.

A constant‐directivity beamforming microphone array

The quality of audio teleconferencing in large rooms and noisy environments can be increased with the use of steerable directional microphone arrays. A minimum bandwidth of 4 oct is required to faithfully transmit the speech signal. In a typical teleconferencing arrangement, only discrete angular directions are of interest and therefore the microphone steering directions are quantized. A standard delay‐sum beamformer can result in noticeable frequency response changes as the talker moves between these steering locations. In an effort to mitigate this problem, a broadband constant‐directivity beamformer has been designed and constructed. A few of the algorithms developed in this work will be discussed and compared to existing techniques. Basically, the solution revolves around the design of FIR filters that are inserted in the delay‐sum beamformer after each element. A constant‐beamwidth 4 oct steerable linear array microphone using directional elements will be described. A real‐time implementation utilizing multiple AT&T DSP3210 digital signal processors is also described.

Frequency-independent beamforming

The beamwidth of a linear array decreases as frequency increases. For broadband beamformers such as microphone arrays for teleconferencing, this frequency dependence implies that signals incident on the outer portions of the main beam are subject to an undesirable lowpass filtering process. In the paper several ways of attaining beamwidth constancy are discussed, including a novel method based on superimposing several marginally steered beams to form a constant beamwidth multi-beam. This method provides an analytically tractable framework for designing realizable constant beamwidth beamformers.<<ETX>>

Nonuniform filterbank design for audio signal modeling

In audio analysis-synthesis based on the sinusoidal model, the signal can be represented as the sum of a deterministic component, which consists of a sum of sinusoids, and a stochastic component, which is a broadband noiselike process, for instance breath noise in a flute. In coding applications, a signal estimate based solely on the deterministic component is often used. For high-fidelity synthesis, however the stochastic component must also be modeled and incorporated into the signal reconstruction. This paper presents a simple approach for designing a nonuniform filterbank based on the properties of the human auditory system; the short-term energies of the subband signals of the nonuniform filterbank provide an effective parameterization of the stochastic component of the signal model.

Atomic signal models based on recursive filter banks

Time-frequency atomic models are useful for signal analysis, modification, and coding, especially when the time-frequency behavior of the atoms matches the behavior of the signal. Such adaptive representations can be derived using the matching pursuit algorithm with an overcomplete dictionary of time-frequency atoms. In this paper, we consider matching pursuit with atoms constructed by coupling causal and anticausal damped sinusoids. These provide advantages over symmetric Gabor atoms for modeling signals with transient behavior, such as music. Furthermore, the matching pursuit computation is simplified by the structure of the atoms; expansions based on these atoms can be derived using simple recursive filter banks.