Download Constrained Pole Optimization for Modal Reverberation The problem of designing a modal reverberator to match a measured room impulse response is considered. The modal reverberator architecture expresses a room impulse response as a parallel combination of resonant filters, with the pole locations determined by the room resonances and decay rates, and the zeros by the source and listener positions. Our method first estimates the pole positions in a frequency-domain process involving a series of constrained pole position optimizations in overlapping frequency bands. With the pole locations in hand, the zeros are fit to the measured impulse response using least squares. Example optimizations for a mediumsized room show a good match between the measured and modeled room responses.
Download FAST MUSIC – An Efficient Implementation Of The Music Algorithm For Frequency Estimation Of Approximately Periodic Signals Noise subspace methods are popular for estimating the parameters of complex sinusoids in the presence of uncorrelated noise and have applications in musical instrument modeling and microphone array processing. One such algorithm, MUSIC (Multiple Signal Classification) has been popular for its ability to resolve closely spaced sinusoids. However, the computational efficiency of MUSIC is relatively low, since it requires an explicit eigenvalue decomposition of an autocorrelation matrix, followed by a linear search over a large space. In this paper, we discuss methods for and the benefits of converting the Toeplitz structure of the autocorrelation matrix to circulant form, so that eigenvalue decomposition can be replaced by a Fast Fourier Transform (FFT) of one row of the matrix. This transformation requires modeling the signal as at least approximately periodic over some duration. For these periodic signals, the pseudospectrum calculation becomes trivial and the accuracy of the frequency estimates only depends on how well periodicity detection works. We derive a closed-form expression for the pseudospectrum, yielding large savings in computation time. We test our algorithm to resolve closely spaced piano partials.
Download Conformal Maps for the Discretization of Analog Filters Near the Nyquist Limit We propose a new analog filter discretization method that is useful
for discretizing systems with features near or above the Nyquist
limit. A conformal mapping approach is taken, and we introduce
the peaking conformal map and shelving conformal map. The proposed method provides a close match to the original analog frequency response below half the sampling rate and is parameterizable, order preserving, and agnostic to the original filter’s order
or type. The proposed method should have applications to discretizing filters that have time-varying parameters or need to be
implemented across many different sampling rates.