Time Fourier Transform

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Juan Antonio Talavera - One of the best experts on this subject based on the ideXlab platform.

  • Short-Time Fourier Transform with the window size fixed in the frequency domain
    Digital Signal Processing, 2018
    Co-Authors: Carlos Mateo, Juan Antonio Talavera
    Abstract:

    Abstract The Short-Time Fourier Transform (STFT) is widely used to convert signals from the Time domain into a Time–frequency representation. This representation has well-known limitations regarding Timefrequency resolution. In this paper we use the basic concept of the Short-Time Fourier Transform, but fix the window size in the frequency domain instead of in the Time domain. This approach is simpler than similar existing methods, such as adaptive STFT and multi-resolution STFT, and in particular it requires neither the band-pass filter banks of multi-resolution techniques, nor the evaluation of local signal characteristics of adaptive techniques. Three case studies are analyzed and the results show that the proposed method allows better identification of signal components compared to standard STFT, multi-resolution STFT and Adaptive Optimal-Kernel Time Frequency Representation, although the method is not computationally efficient in its present form. Some synthetic and real world signals are used to demonstrate the effectiveness of the proposed technique.

  • Short-Time Fourier Transform with the Window Size Fixed in the Frequency Domain (STFT-FD): Implementation
    SoftwareX, 2018
    Co-Authors: Carlos Mateo, Juan Antonio Talavera
    Abstract:

    Abstract The Short-Time Fourier Transform (STFT) is widely used to convert signals from the Time domain into a Time–frequency representation. This representation has well known limitations regarding Timefrequency resolution. In this paper, we present a set of MATLAB functions to compute a Transform, which uses the basic concept of the Short-Time Fourier Transform, but fixes the window size in the frequency domain instead of in the Time domain. This approach is simpler than similar existing methods, such as adaptive STFT or multi-resolution STFT, and in particular it requires neither the filters of multi-resolution techniques, nor the evaluation of the local signal characteristics of adaptive techniques. An illustrative example is presented and compared with the Morlet wavelet Transform.

Ruairi De Frein - One of the best experts on this subject based on the ideXlab platform.

  • The Synchronized Short-Time-Fourier-Transform: Properties and Definitions for Multichannel Source Separation
    IEEE Transactions on Signal Processing, 2011
    Co-Authors: Ruairi De Frein, Scott Rickard
    Abstract:

    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.

  • Adapting Bases Using the Synchronized Short Time Fourier Transform and Non-negative Matrix Factorization
    2009
    Co-Authors: Ruairi De Frein
    Abstract:

    Adapting Bases Using the Synchronized Short Time Fourier Transform and Non-negative Matrix Factorization

Carlos Mateo - One of the best experts on this subject based on the ideXlab platform.

  • Short-Time Fourier Transform with the window size fixed in the frequency domain
    Digital Signal Processing, 2018
    Co-Authors: Carlos Mateo, Juan Antonio Talavera
    Abstract:

    Abstract The Short-Time Fourier Transform (STFT) is widely used to convert signals from the Time domain into a Time–frequency representation. This representation has well-known limitations regarding Timefrequency resolution. In this paper we use the basic concept of the Short-Time Fourier Transform, but fix the window size in the frequency domain instead of in the Time domain. This approach is simpler than similar existing methods, such as adaptive STFT and multi-resolution STFT, and in particular it requires neither the band-pass filter banks of multi-resolution techniques, nor the evaluation of local signal characteristics of adaptive techniques. Three case studies are analyzed and the results show that the proposed method allows better identification of signal components compared to standard STFT, multi-resolution STFT and Adaptive Optimal-Kernel Time Frequency Representation, although the method is not computationally efficient in its present form. Some synthetic and real world signals are used to demonstrate the effectiveness of the proposed technique.

  • Short-Time Fourier Transform with the Window Size Fixed in the Frequency Domain (STFT-FD): Implementation
    SoftwareX, 2018
    Co-Authors: Carlos Mateo, Juan Antonio Talavera
    Abstract:

    Abstract The Short-Time Fourier Transform (STFT) is widely used to convert signals from the Time domain into a Time–frequency representation. This representation has well known limitations regarding Timefrequency resolution. In this paper, we present a set of MATLAB functions to compute a Transform, which uses the basic concept of the Short-Time Fourier Transform, but fixes the window size in the frequency domain instead of in the Time domain. This approach is simpler than similar existing methods, such as adaptive STFT or multi-resolution STFT, and in particular it requires neither the filters of multi-resolution techniques, nor the evaluation of the local signal characteristics of adaptive techniques. An illustrative example is presented and compared with the Morlet wavelet Transform.

Sylvain Meignen - One of the best experts on this subject based on the ideXlab platform.

Scott Rickard - One of the best experts on this subject based on the ideXlab platform.

  • The Synchronized Short-Time-Fourier-Transform: Properties and Definitions for Multichannel Source Separation
    IEEE Transactions on Signal Processing, 2011
    Co-Authors: Ruairi De Frein, Scott Rickard
    Abstract:

    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.