24,949 research outputs found

    Underdetermined-order recursive least-squares adaptive filtering: The concept and algorithms

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    A kepstrum approach to filtering, smoothing and prediction

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    The kepstrum (or complex cepstrum) method is revisited and applied to the problem of spectral factorization where the spectrum is directly estimated from observations. The solution to this problem in turn leads to a new approach to optimal filtering, smoothing and prediction using the Wiener theory. Unlike previous approaches to adaptive and self-tuning filtering, the technique, when implemented, does not require a priori information on the type or order of the signal generating model. And unlike other approaches - with the exception of spectral subtraction - no state-space or polynomial model is necessary. In this first paper results are restricted to stationary signal and additive white noise

    On the Equivalence of the Digital Waveguide and Finite Difference Time Domain Schemes

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    It is known that the digital waveguide (DW) method for solving the wave equation numerically on a grid can be manipulated into the form of the standard finite-difference time-domain (FDTD) method (also known as the ``leapfrog'' recursion). This paper derives a simple rule for going in the other direction, that is, converting the state variables of the FDTD recursion to corresponding wave variables in a DW simulation. Since boundary conditions and initial values are more intuitively transparent in the DW formulation, the simple means of converting back and forth can be useful in initializing and constructing boundaries for FDTD simulations.Comment: v1: 6 pages; v2: 7 pages, generally more polished, more examples, expanded discussion; v3: 15 pages, added state space formulation, analysis of inputs and boundary conditions, translation of passive boundary conditions; v4: various typos fixe

    Efficient Synthesis of Room Acoustics via Scattering Delay Networks

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    An acoustic reverberator consisting of a network of delay lines connected via scattering junctions is proposed. All parameters of the reverberator are derived from physical properties of the enclosure it simulates. It allows for simulation of unequal and frequency-dependent wall absorption, as well as directional sources and microphones. The reverberator renders the first-order reflections exactly, while making progressively coarser approximations of higher-order reflections. The rate of energy decay is close to that obtained with the image method (IM) and consistent with the predictions of Sabine and Eyring equations. The time evolution of the normalized echo density, which was previously shown to be correlated with the perceived texture of reverberation, is also close to that of IM. However, its computational complexity is one to two orders of magnitude lower, comparable to the computational complexity of a feedback delay network (FDN), and its memory requirements are negligible

    The Stationary Phase Approximation, Time-Frequency Decomposition and Auditory Processing

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    The principle of stationary phase (PSP) is re-examined in the context of linear time-frequency (TF) decomposition using Gaussian, gammatone and gammachirp filters at uniform, logarithmic and cochlear spacings in frequency. This necessitates consideration of the use the PSP on non-asymptotic integrals and leads to the introduction of a test for phase rate dominance. Regions of the TF plane that pass the test and don't contain stationary phase points contribute little or nothing to the final output. Analysis values that lie in these regions can thus be set to zero, i.e. sparsity. In regions of the TF plane that fail the test or are in the vicinity of stationary phase points, synthesis is performed in the usual way. A new interpretation of the location parameters associated with the synthesis filters leads to: (i) a new method for locating stationary phase points in the TF plane; (ii) a test for phase rate dominance in that plane. Together this is a TF stationary phase approximation (TFSFA) for both analysis and synthesis. The stationary phase regions of several elementary signals are identified theoretically and examples of reconstruction given. An analysis of the TF phase rate characteristics for the case of two simultaneous tones predicts and quantifies a form of simultaneous masking similar to that which characterizes the auditory system.Comment: Submitted to IEEE Trans Signal Processing 14th Aug 201
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