A modification of the spectrogram (log magnitude of the short-time Fourier transform) to more accurately show the instantaneous frequencies of signal components was first proposed in 1976 [Kodera et al., Phys. Earth Planet. Inter. 12, 142-150 (1976)], and has been considered or reinvented a few times since but never widely adopted. This paper presents a unified theoretical picture of this time-frequency analysis method, the time-corrected instantaneous frequency spectrogram, together with detailed implementable algorithms comparing three published techniques for its computation. The new representation is evaluated against the conventional spectrogram for its superior ability to track signal components. The lack of a uniform framework for either mathematics or implementation details which has characterized the disparate literature on the schemes has been remedied here. Fruitful application of the method is shown in the realms of speech phonation analysis, whale song pitch tracking, and additive sound modeling.

We \vill present research associated }vith the sound modeling soft$~rare called Lemur. In Lemur, Jve have developed a ne}v extension LOthe sinusoidal modeling technique of McAulay and Qua~ieri to accommodate sounds having significant non-sinusoidal energy.

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Modulation filtering is a technique for filtering slowly-varying envelopes of frequency subbands of a signal, without affecting the signal's phase and fine-structure. Coherent modulation filtering is a promising subtype of such techniques where subband envelopes are determined through demodulation of the subband signal with a coherently detected subband carrier. In this paper we propose a coherent modulation filtering technique that detects the carriers using the frequency reassignment (FR) operator from timefrequency reassignment. We show how this technique avoids the use of finite differences in the computation of instantaneous frequency (IF), and that it estimates IF more accurately than a past technique as a result. We confirm that the FR-enhanced technique retains the desirable modulation filtering properties (superposition and the preservation of zero-crossings) and show that it performs better on the same single-channel music source separation task than the past technique.

The reassigned bandwidth-enhanced additive sound model is a high-delity sound representation that allows manipulations and transformations to be applied to a great variety of sounds, including noisy and inharmonic sounds. Combining sinusoidal and noise energy in a homogeneous representation, the reassigned bandwidth-enhanced model is ideally suited to sound morphing and is implemented in the open-source software library Loris. This article presents methods for using Loris and the reassigned bandwidth-enhanced additive model to achieve high-delity sound representations and manipulations, and it introduces software tools that allow programmers (in C/C``and various scripting languages) and non-programmers to use the sound modeling and manipulation capabilities of the Loris package.The reassigned bandwidth-enhanced additive model is similar in spirit to traditional sinusoidal models (McAulay and Quatieri 1986;Serra and Smith 1990;Fitz and Haken 1996) in that a waveform is modeled as a collection of components, called partials, having time-varying amplitude and frequency envelopes. Our partials are not strictly sinusoidal, however. We employ a technique of bandwidth enhancement to combine sinusoidal energy and noise energy into a single partial having time-varying frequency, amplitude, and noisiness (or bandwidth) parameters (Fitz, Haken, and Christensen 2000a). The bandwidth envelope allows us to de ne a single component type that can be used to manipulate both sinusoidal and noisy parts of sound in an intuitive way. The encoding of noise associated with a bandwidth-enhanced partial is robust under time dilation and other model-domain transformations, and it is independent of other partials in the representation.We use the method of reassignment (Auger and Flandrin 1995) to improve the time and frequency estimates used to de ne our partial parameter envelopes. The breakpoints for the partial parameter envelopes are obtained by following ridges on a reassigned time-frequency surface. Our algorithm shares with traditional sinusoidal methods the notion of temporally connected partial parameter estimates, but by contrast, our estimates are non-uniformly distributed in both time and frequency. This model yields greater resolution in time and frequency than is possible using conventional additive techniques and preserves the temporal envelope of transient signals, even in modi ed reconstruction (Fitz, Haken, and Christensen 2000b).