Sine wave

About: Sine wave is a(n) research topic. Over the lifetime, 12183 publication(s) have been published within this topic receiving 93013 citation(s). The topic is also known as: sinusoid.

Speech analysis/Synthesis based on a sinusoidal representation

Abstract: A sinusoidal model for the speech waveform is used to develop a new analysis/synthesis technique that is characterized by the amplitudes, frequencies, and phases of the component sine waves. These parameters are estimated from the short-time Fourier transform using a simple peak-picking algorithm. Rapid changes in the highly resolved spectral components are tracked using the concept of "birth" and "death" of the underlying sine waves. For a given frequency track a cubic function is used to unwrap and interpolate the phase such that the phase track is maximally smooth. This phase function is applied to a sine-wave generator, which is amplitude modulated and added to the other sine waves to give the final speech output. The resulting synthetic waveform preserves the general waveform shape and is essentially perceptually indistinguishable from the original speech. Furthermore, in the presence of noise the perceptual characteristics of the speech as well as the noise are maintained. In addition, it was found that the representation was sufficiently general that high-quality reproduction was obtained for a larger class of inputs including: two overlapping, superposed speech waveforms; music waveforms; speech in musical backgrounds; and certain marine biologic sounds. Finally, the analysis/synthesis system forms the basis for new approaches to the problems of speech transformations including time-scale and pitch-scale modification, and midrate speech coding [8], [9].

The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms

Abstract: The Lomb-Scargle periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to least-squares fitting of sine waves. We give an analytic solution for the generalisation to a full sine wave fit, including an offset and weights (χ 2 fitting). Compared to the Lomb-Scargle periodogram, the generalisation is superior as it provides more accurate frequencies, is less susceptible to aliasing, and gives a much better determination of the spectral intensity. Only a few modifications are required for the computation and the computational effort is similar. Our approach brings together several related methods that can be found in the literature, viz. the date-compensated discrete Fourier transform, the floating-mean periodogram, and the “spectral significance” estimator used in the SigSpec program, for which we point out some equivalences. Furthermore, we present an algorithm that implements this generalisation for the evaluation of the Keplerian periodogram that searches for the period of the best-fitting Keplerian orbit to radial velocity data. The systematic and non-random algorithm is capable of detecting eccentric orbits, which is demonstrated by two examples and can be a useful tool in searches for the orbital periods of exoplanets.

Accurate short-term analysis of the fundamental frequency and the harmonics-to-noise ratio of a sampled sound

Abstract: We present a straightforward and robust algorithm for periodicity detection, working in the lag (autocorrelation) domain. When it is tested for periodic signals and for signals with additive noise or jitter, it proves to be several orders of magnitude more accurate than the methods commonly used for speech analysis. This makes our method capable of measuring harmonics-to-noise ratios in the lag domain with an accuracy and reliability much greater than that of any of the usual frequency-domain methods. By definition, the best candidate for the acoustic pitch period of a sound can be found from the position of the maximum of the autocorrelation function of the sound, while the degree of periodicity (the harmonics-to-noise ratio) of the sound can be found from the relative height of this maximum. However, sampling and windowing cause problems in accurately determining the position and height of the maximum. These problems have led to inaccurate timedomain and cepstral methods for pitch detection, and to the exclusive use of frequency-domain methods for the determination of the harmonics-to-noise ratio. In this paper, I will tackle these problems. Table 1 shows the specifications of the resulting algorithm for two spectrally maximally different kinds of periodic sounds: a sine wave and a periodic pulse train; other periodic sounds give results between these. Table 1. The accuracy of the algorithm for a sampled sine wave and for a correctly sampled periodic pulse train, as a function of the number of periods that fit in the duration of a Hanning window. These results are valid for pitch frequencies up to 80% of the Nyquist frequency. These results were measured for a sampling frequency of 10 kHz and window lengths of 40 ms (for pitch) and 80 ms (for HNR), but generalize to other sampling frequencies and window lengths (see section 5).

Statistical properties of a sine wave plus random noise

Abstract: In Some technical problems we are concerned with a current which consists of a sinusoidal component plus a random noise component. A number of statistical properties of such a current are given here. The present paper may be regarded as an extension of Section 3.10 of an earlier paper,1 “Mathematical Analysis of Random Noise”, where some of the simpler properties of a sine wave plus random noise are discussed.

Patch-clamp techniques for time-resolved capacitance measurements in single cells.

Abstract: Two methods are described for estimation of passive cell parameters such as membrane capacitance, membrane conductance and access resistance in tight-seal whole cell recording. Both methods are restricted in their application to cases where the cell under study can be approximated by a simple three-component network with linear properties over some voltage range. One method, referred to as the time domain technique, requires only standard electrophysiological equipment and a computer. Parameters are derived from an analysis of capacitive transients during square wave stimulation. It is readily adaptable to wide variations in experimental parameters. Particurlarly, it is equally applicable to the “slow whole-cell” configuration (access resistance in the range 100 MΩ to 1 GΩ) and to normal whole-cell measurements (access resistance typically 10 MΩ). The other method applies a sine wave command signal to the cell and employs a lock-in amplifier to analyse the resulting current signal. Two modes of operating the lock-in amplifier are described. One mode provides an output signal directly proportional to small changes in capacitance at maximum resolution (1–10 fF). The other mode, in conjunction with a digital computer, supplies estimates of all passive cell parameters, as does the time domain technique, but with a large amount of data reduction performed by the lock-in amplifier itself. Due to the special hardware, however, this method is not as flexible as the time domain technique.