S.H. Nawab

Identification of musical chords using CONSTANT-Q spectra

We present an approach to the extraction of frequencies corresponding to chords in western polyphonic music. In the first phase of this approach constant-Q spectral analysts directly provides the features from which the fundamental frequencies for 43 of the 57 possible categories of chords can be extracted without ambiguity. Each remaining chord category has a potential ambiguity associated with it because of frequency resolution problems The second phase of our approach is designed to address such ambiguities. A software implementation of our approach was used successfully to validate its performance on a representative set of polyphonic musical signals.

Efficient STFT approximation using a quantization and differencing method

A class of algorithms for efficiently computing approximations to the short-time Fourier transform (STFT) of any given signal is introduced. These algorithms may be classified in accordance with the number of quantization levels they use to represent the values in each short-time frame of the input signal. The structure and properties of these algorithms are illustrated through a specific case which uses a three-level quantization in each frame. Results obtained by applying an implementation of the three-level algorithm to musical and speech signals are also presented. The resulting approximations conform to the theoretical expectations of a 9-dB SNR in the STFT approximations. However, these approximations are found to require an order-of-magnitude-less computation than fast Fourier transform (FFT)-based algorithms for the exact STFT.<<ETX>>

Extended model variety analysis for integrated processing and understanding of signals

The authors extend their previous work (Nawab and Lesser, 1991; Weiss et al., 1991) on model variety analysis of a signal processing algorithm with respect to the class of all input signals that may potentially arise in a given signal understanding application. This analysis has two related objectives. The first objective is to partition the set of all possible signals in the application domain into two sets according to whether each signal is correctly or incorrectly processed by the signal processing algorithm under consideration. The second objective of model variety analysis is to characterize the nature of the distortions in the signal processing output for the cases where the input signal is incorrectly processed. The results of model variety analysis are useful for designing signal understanding systems for applications where it is necessary for the signal processing to be carried out in a situation-dependent manner. Model variety analysis and its usefulness for the design of signal understanding systems are illustrated through examples involving the use of short-time Fourier transform (STFT) processing for a sound understanding application.<<ETX>>

Approximate signal processing using incremental refinement and deadline-based algorithms

A framework for approximate signal processing is introduced which can be used to design novel classes of algorithms for performing DFT and STFT calculations. In particular, we focus on the derivation of multi-stage incremental refinement algorithms that meet a variety of design criteria on the tradeoff achieved at each stage between solution quality and computational cost.

The classification of ringing sounds

The problem of ringing sound (e.g. telephone, alarm clock, etc.) classification is addressed. A time-domain model, exhibiting the phenomenon of interference is found to have behavior similar to that exhibited by a telephone ringing sound. This motivates a frequency-domain production model which asserts that ringing sounds can be modeled as bandpass-filtered white noise, where the filter has a power spectral density in the form of isosceles triangles. A parameter estimation technique based on this model is found to provide enough information to classify ringing sounds.<<ETX>>

Probabilistic complexity analysis of incremental DFT algorithms

We present a probabilistic complexity analysis of a class of multi-stage algorithms for computing successive approximations to the DFT. While the quality of the approximate spectra obtained after any stage of these algorithms can be readily quantified in terms of commonly used input-independent metrics of spectral quality, each stages arithmetic complexity is dependent on the nature of the input signal. Modeling the input signal as a stationary Gaussian-distributed random process, we obtain estimates of the distribution of the number of arithmetic operations required to complete any algorithm stage. This enables the derivation of important design information such as the probability with which a desired quality of approximation is achieved within a given arithmetic bound. Our results are verified using a Monte Carlo analysis.

Filter transitions in adaptive IIR approximate filtering

The effects associated with the switching of filter orders in an incrementally adaptive IIR approximate filtering technique are evaluated in the context of speech signals. Through listening experiments, we have found that the perceptual quality of the speech at the filter output is sensitive to the initial conditions used in initiating a transition to a higher filter order. If zero initial conditions are used there is a significant crackling sound due to error bursts at points where switches to higher order filters take place. If output samples from the pre-transition filter are used as initial conditions for the post-transition filter, the amplitude of the error bursts decreases significantly. An analysis is presented to account for these observations.

Integration of DSP algorithms and musical constraints for the separation of partials in polyphonic music

We illustrate how high-level knowledge from the musical domain may be integrated with sophisticated signal processing algorithms within a system for separating possibly overlapping partial frequency components from polyphonic music. Musical knowledge utilized in our system is in the form of constraints on the time-frequency behavior of musical signals such as the frequency locations of notes on the western musical scale and the presence or absence of vibrato in each note. For any given signal scenario, these constraints help in appropriately initializing and adjusting a set of algorithms for constant-Q processing, spectral peak picking, and multihypothesis tracking through Kalman filtering. As demonstrated by the evaluation of our system with a variety of signals containing two simultaneously played violin notes, the application of these algorithms results in the accurate separation of individual partials.

Time-frequency analysis of non-stationary harmonic sounds

An approach to the analysis of nonstationary harmonic sounds accompanied by other possibly nonstationary sounds is introduced. In this approach, one first computes the magnitude square of the short-time Fourier transform (MSQ-STFT) with exponential frequency sampling. A technique based on principal components analysis is then applied to the MSQ-STFT of the signal data. Under a broadly applicable set of conditions, this analysis produces a time-frequency distribution in which components of the interfering sounds are suppressed relative to the components of the harmonic sound of interest. Experimental results on real sounds and synthetic signals are presented to illustrate the practical success of this approach.<<ETX>>

Integration of STFT and Wigner analysis in a knowledge-based system for sound understanding

The authors describe and demonstrate how the combined use of Wigner and short-time Fourier transform (STFT) processing can be used to advantage in a sound understanding application. Specifically, the Wigner processing of a signal is used for alerting the signal understanding system to the possibility of inadequate time or frequency resolution in the STFT processing of the same signal. The signal understanding system may then reprocess the signal with an STFT with a different window length. The knowledge-based control required for carrying out such signal processing is available in a sound understanding system in the context of which this research was carried out.<<ETX>>