Refining a Phase Vocoder for Vocal Modulation

Vocal harmonies are a highly sought-after effect in the music industry, as they allow singers to portray more emotion and meaning through their voices. The chords one hears when listening to nearly any modern song are constructed through common ratios of frequencies (e.g., the recipe for a major triad is 4:5:6). Currently, vocal melodies are only readily obtainable through a few methods, including backup singers, looper-effects systems, and post-process overdubbing. The issue with these is that there is currently no publicly-available code that allows solo-artists to modulate input audio to whatever chord structure is desired while maintaining the same duration and timbre in the successive layers. This thesis plans to address this issue using the phase vocoder method. If this modulation technique is successful, this could revolutionize the way vocalists perform. The introduction of real-time self harmonization would allow artists to have access to emphasized lyrical phrases and vocals without needing to hire and train backup vocalists. This phase vocoder would also allow for more vocal improvisation, as the individual would only need to know how to harmonize with themselves and would thus not be relying on interpreting how backup vocalists plan on moving the melody when creating more spontaneously

Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames

We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph wavelet constructions are only adapted to the length of the spectrum, the filters proposed in this paper are adapted to the distribution of graph Laplacian eigenvalues, and therefore lead to atoms with better discriminatory power. Our approach is to first characterize a family of systems of uniformly translated kernels in the graph spectral domain that give rise to tight frames of atoms generated via generalized translation on the graph. We then warp the uniform translates with a function that approximates the cumulative spectral density function of the graph Laplacian eigenvalues. We use this approach to construct computationally efficient, spectrum-adapted, tight vertex-frequency and graph wavelet frames. We give numerous examples of the resulting spectrum-adapted graph filters, and also present an illustrative example of vertex-frequency analysis using the proposed construction

The Synchronized Short-Time-Fourier-Transform: Properties and Definitions for Multichannel Source Separation.

This paper proposes the use of a synchronized linear transform, the synchronized short-time-Fourier-transform (sSTFT), for time-frequency analysis of anechoic mixtures. We address the short comings of the commonly used time-frequency linear transform in multichannel settings, namely the classical short-time-Fourier-transform (cSTFT). We propose a series of desirable properties for the linear transform used in a multichannel source separation scenario: stationary invertibility, relative delay, relative attenuation, and finally delay invariant relative windowed-disjoint orthogonality (DIRWDO). Multisensor source separation techniques which operate in the time-frequency domain, have an inherent error unless consideration is given to the multichannel properties proposed in this paper. The sSTFT preserves these relationships for multichannel data. The crucial innovation of the sSTFT is to locally synchronize the analysis to the observations as opposed to a global clock. Improvement in separation performance can be achieved because assumed properties of the time-frequency transform are satisfied when it is appropriately synchronized. Numerical experiments show the sSTFT improves instantaneous subsample relative parameter estimation in low noise conditions and achieves good synthesis

Coherently combining short data segments for all-sky semi-coherent continuous gravitational wave searches

We present a method for coherently combining short data segments from gravitational-wave detectors to improve the sensitivity of semi-coherent searches for continuous gravitational waves. All-sky searches for continuous gravitational waves from unknown sources are computationally limited. The semi-coherent approach reduces the computational cost by dividing the entire observation timespan into short segments to be analyzed coherently, then combined together incoherently. Semi-coherent analyses that attempt to improve sensitivity by coherently combining data from multiple detectors face a computational challenge in accounting for uncertainties in signal parameters. In this article, we lay out a technique to meet this challenge using summed Fourier transform coefficients. Applying this technique to one all-sky search algorithm called TwoSpect, we confirm that the sensitivity of all-sky, semi-coherent searches can be improved by coherently combining the short data segments. For misaligned detectors, however, this improvement requires careful attention when marginalizing over unknown polarization parameters. In addition, care must be taken in correcting for differential detector velocity due to the Earth's rotation for high signal frequencies and widely separated detectors.Comment: 15 pages, 3 figures, 1 tabl

Frequency-domain P-approximant filters for time-truncated inspiral gravitational wave signals from compact binaries

Frequency-domain filters for time-windowed gravitational waves from inspiralling compact binaries are constructed which combine the excellent performance of our previously developed time-domain P-approximants with the analytic convenience of the stationary phase approximation without a serious loss in event rate. These Fourier-domain representations incorporate the ``edge oscillations'' due to the (assumed) abrupt shut-off of the time-domain signal caused by the relativistic plunge at the last stable orbit. These new analytic approximations, the SPP-approximants, are not only `effectual' for detection and `faithful' for parameter estimation, but are also computationally inexpensive to generate (and are `faster' by factors up to 10, as compared to the corresponding time-domain templates). The SPP approximants should provide data analysts the Fourier-domain templates for massive black hole binaries of total mass m less than about 40 solar mases, the most likely sources for LIGO and VIRGO.Comment: 50 Pages, 10 Postscript figures, 7 Tables, Revtex, Typos corrected, References updated, Additions on pages 25, 26 and 3

Audio Analysis/synthesis System

A method and apparatus for the automatic analysis, synthesis and modification of audio signals, based on an overlap-add sinusoidal model, is disclosed. Automatic analysis of amplitude, frequency and phase parameters of the model is achieved using an analysis-by-synthesis procedure which incorporates successive approximation, yielding synthetic waveforms which are very good approximations to the original waveforms and are perceptually identical to the original sounds. A generalized overlap-add sinusoidal model is introduced which can modify audio signals without objectionable artifacts. In addition, a new approach to pitch-scale modification allows for the use of arbitrary spectral envelope estimates and addresses the problems of high-frequency loss and noise amplification encountered with prior art methods. The overlap-add synthesis method provides the ability to synthesize sounds with computational efficiency rivaling that of synthesis using the discrete short-time Fourier transform (DSTFT) while eliminating the modification artifacts associated with that method.Georgia Tech Research Corporatio

Adaptive phase-shifting algorithm for temporal phase evaluation

Most standard temporal phase-shifting algorithms evaluate the phase by computing a windowed Fourier transform (WFT) of the intensity signal at the carrier frequency of the system. However, displacement of the specimen during image acquisition may cause the peak of the transform to shift away from the carrier frequency, leading to phase errors and even unwrapping failure. We present a novel TPS method that searches for the peak of the WFT and evaluates the phase at that frequency instead of at the carrier frequency. The performance of this method is compared with that of standard algorithms by using numerical simulations. Experimental results from highspeed speckle interferometry studies of carbon fiber panels are also presented