Topic
Time–frequency analysis
About: Time–frequency analysis is a research topic. Over the lifetime, 5407 publications have been published within this topic receiving 104346 citations.
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TL;DR: This method encompasses the conventional minimum mean-squared error beamforming in the frequency domain or spatial domain as special cases and is especially useful for applications involving chirp signals such as signal enhancement problems with accelerating sinusoidal sources.
Abstract: We present a new method of beamforming using the fractional Fourier transform (FrFT). This method encompasses the conventional minimum mean-squared error (MMSE) beamforming in the frequency domain or spatial domain as special cases. It is especially useful for applications involving chirp signals such as signal enhancement problems with accelerating sinusoidal sources where the Doppler effect generates chirp signals and a frequency shift and active radar problems where chirp signals are transmitted. Numerical examples demonstrate the potential advantage of the proposed method over the ordinary frequency or spatial domain beamforming for a moving source scenario.
72 citations
TL;DR: The most efficient of the reviewed methods, which uses the Zak transform as an operational calculus, performs Gabor analysis and synthesis transforms with complexity of the same order as a fast Fourier transform (FFT).
Abstract: Equations for the continuous-parameter Gabor transform are presented and converted to finite discrete form suitable for digital computation. A comparative assessment of the computational complexity of several algorithms that execute the finite discrete equations is given, with results in the range O ( P 2 ) to O ( P log, P), where P is the number of input data points being transformed. The most efficient of the reviewed methods, which uses the Zak transform as an operational calculus, performs Gabor analysis and synthesis transforms with complexity of the same order as a fast Fourier transform (FFT).
72 citations
TL;DR: An extensive bibliographic review of applications of WTs in the measurement and analysis of harmonic distortion in power systems is presented, discussing the performance of the different methods proposed in the technical literature.
Abstract: Wavelet transform (WT) is one of the most useful digital signal processing tools for time-frequency analysis of power quality disturbances in power systems. This paper presents an extensive bibliographic review of applications of WTs in the measurement and analysis of harmonic distortion in power systems, discussing the performance of the different methods proposed in the technical literature.
72 citations
01 Dec 1996
TL;DR: The major time and frequency analysis methods that have been applied to music processing are traced and application areas described as discussed by the authors, and the limitations of windowing methods and their reliance on steady-state assumptions and infinite duration sinusoids to define frequency and amplitude are detailed.
Abstract: The major time and frequency analysis methods that have been applied to music processing are traced and application areas described. Techniques are examined in the context of Cohen's class, facilitating comparison and the design of new approaches. A trumpet example illustrates most techniques. The impact of different analysis methods on pitch and timbre examination is shown. Analyses spanning Fourier series and transform, pitch synchronous analysis, heterodyne filter, short-time Fourier transform (STFT), phase vocoder, constant-Q and wavelet transforms, the Wigner (1932) distribution, and the modal distribution are all covered. The limitations of windowing methods and their reliance on steady-state assumptions and infinite duration sinusoids to define frequency and amplitude are detailed. The Wigner distribution, in contrast, uses the analytic signal to define instantaneous frequency and power parameters. The modal distribution is shown to be a linear transformation of the Wigner distribution optimized for estimating those parameters for a musical signal model. Application areas consider analysis, resynthesis, transcription, and visualization. The more stringent requirements for time-frequency (TF) distributions in these applications are compared with the weaker requirements found in speech analysis and highlight the need for further theoretical research.
72 citations
TL;DR: Results show that bionic wavelet transform performs better than WT in these three aspects, and that BWT is appropriate for speech signal processing, especially for cochlear implants.
Abstract: A new adaptive wavelet transform, named bionic wavelet transform (BWT), is developed based on a model of the active auditory system. The most distinguishing characteristic of BWT is that its resolution in the time-frequency domain can be adaptively adjusted not only by the signal frequency but also by the signal instantaneous amplitude and its first-order differential. The automatically adjusted resolution, even in a fixed frequency along the time-axis, is achieved by introducing the active control of the auditory system into the wavelet transform (WT). Other properties of BWT include that: 1) BWT is a nonlinear transform that has high sensitivity and frequency selectivity; 2) BWT represents the signal with a concentrated energy distribution; and 3) the inverse BWT can reconstruct the original signal from its time-frequency representation. In order to compare these three properties between BWT and WT, experiments were conducted on both constructed signals and real speech signals. The results show that BWT performs better than WT in these three aspects, and that BWT is appropriate for speech signal processing, especially for cochlear implants.
72 citations