Squared Magnitude

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G F Boudreauxbartels - One of the best experts on this subject based on the ideXlab platform.

  • a comparison of the existence of cross terms in the wigner distribution and the Squared Magnitude of the wavelet transform and the short time fourier transform
    IEEE Transactions on Signal Processing, 1992
    Co-Authors: S. Kadambe, G F Boudreauxbartels
    Abstract:

    It is shown that cross terms comparable to those found in the Wigner distribution (WD) exist for the energy distributions of the wavelet transform (WT) and the short-time Fourier transform (STFT). The geometry of the cross terms is described by deriving mathematical expressions for the energy distributions of the STFT and the WT of a multicomponent signal. From those mathematical expressions it is inferred that the STFT and the WT cross terms: (1) occur at the intersection of the respective transforms of the two signals under consideration, whereas the WD cross terms occur at mid-time-frequency of the two signals; (2) are oscillatory in nature, as are the WD cross terms, and are modulated by a cosine whose argument is a function of the difference in center times and center frequencies of the signals under consideration; and (3) can have a maximum amplitude as large as twice the product of the Magnitude of the transforms of the two signals in question, like WD cross terms. It is shown that the presence of these cross terms could lead to problems in analyzing a multicomponent signal. The consequences of this effect with respect to speech applications are discussed. >

Rainer Martin - One of the best experts on this subject based on the ideXlab platform.

  • mmse estimation of Magnitude Squared dft coefficients with supergaussian priors
    International Conference on Acoustics Speech and Signal Processing, 2003
    Co-Authors: Colin Breithaupt, Rainer Martin
    Abstract:

    We present two minimum mean square error (MMSE) frequency domain estimators of the Squared Magnitude of a clean speech signal that is degraded by additive noise. These estimators are derived under the assumption that the DFT (discrete Fourier transform) coefficients of the clean speech are best modelled by the Gamma probability distribution function (PDF) instead of the common Gaussian PDF. The statistics of the perturbing noise is the Gaussian PDF in one case and the Laplacian PDF in the other. The estimators are used as noise reduction filters in the experimental evaluation. We give a comparison with a previously derived estimator which uses the Gaussian PDF as the PDF for speech and noise coefficients.

  • ICASSP (1) - MMSE estimation of Magnitude-Squared DFT coefficients with superGaussian priors
    2003 IEEE International Conference on Acoustics Speech and Signal Processing 2003. Proceedings. (ICASSP '03)., 1
    Co-Authors: Colin Breithaupt, Rainer Martin
    Abstract:

    We present two minimum mean square error (MMSE) frequency domain estimators of the Squared Magnitude of a clean speech signal that is degraded by additive noise. These estimators are derived under the assumption that the DFT (discrete Fourier transform) coefficients of the clean speech are best modelled by the Gamma probability distribution function (PDF) instead of the common Gaussian PDF. The statistics of the perturbing noise is the Gaussian PDF in one case and the Laplacian PDF in the other. The estimators are used as noise reduction filters in the experimental evaluation. We give a comparison with a previously derived estimator which uses the Gaussian PDF as the PDF for speech and noise coefficients.

Ralf Vick - One of the best experts on this subject based on the ideXlab platform.

S. Kadambe - One of the best experts on this subject based on the ideXlab platform.

  • a comparison of the existence of cross terms in the wigner distribution and the Squared Magnitude of the wavelet transform and the short time fourier transform
    IEEE Transactions on Signal Processing, 1992
    Co-Authors: S. Kadambe, G F Boudreauxbartels
    Abstract:

    It is shown that cross terms comparable to those found in the Wigner distribution (WD) exist for the energy distributions of the wavelet transform (WT) and the short-time Fourier transform (STFT). The geometry of the cross terms is described by deriving mathematical expressions for the energy distributions of the STFT and the WT of a multicomponent signal. From those mathematical expressions it is inferred that the STFT and the WT cross terms: (1) occur at the intersection of the respective transforms of the two signals under consideration, whereas the WD cross terms occur at mid-time-frequency of the two signals; (2) are oscillatory in nature, as are the WD cross terms, and are modulated by a cosine whose argument is a function of the difference in center times and center frequencies of the signals under consideration; and (3) can have a maximum amplitude as large as twice the product of the Magnitude of the transforms of the two signals in question, like WD cross terms. It is shown that the presence of these cross terms could lead to problems in analyzing a multicomponent signal. The consequences of this effect with respect to speech applications are discussed. >

  • A Comparison of the Existence of "Cross Terms" in the Wigner Distribution and the Squared Magnitude of the Wavelet Transform and the Short Time
    1992
    Co-Authors: S. Kadambe, G. Faye Boudreaux-bartels
    Abstract:

    The wavelet transform (WT), a time-scale repre- sentation, is linear by definition. However, the nonlinear en- ergy distribution of this transform is often used to represent the signal; it contains ''cross terms" which could cause prob- lems while analyzing multicomponent signals. In this paper, we show that the cross terms that exist in the energy distribution of the WT are comparable with those found in the Wigner dis- tribution (WD), a quadratic time-frequency representation, and the energy distribution of the short time Fourier transform (STFT), of closely spaced signals. The cross terms of the WT and the STFT energy distributions occur at the intersection of their respective WT and STFT spaces, while for the WD they occur midtime and midfrequency. The parameters of the cross terms are a function of the difference in center frequencies and center times of the perpended signals. The amplitude of these cross terms can be as large as twice the product of the magni- tudes of the transforms of the two signals in question in all three cases. In this paper, we consider the significance of the effect of the cross terms on the analysis of a multicomponent signal in each of these three representations. We also compare the advantages and disadvantages of all of these methods in appli- cations to signal processing.

Jyh-yeong Chang - One of the best experts on this subject based on the ideXlab platform.

  • Model reduction for continuous- and discrete-time systems via Squared-Magnitude responses matching by linear programming
    International Journal of Systems Science, 1991
    Co-Authors: Mu-huo Cheng, Jyh-yeong Chang
    Abstract:

    The use of linear programming technique for the model reduction of continuous-and discrete-time systems is discussed. Based on Squared-Magnitude responses between the original system and its reduced model, a novel error function is presented. Two linear programming formulations are presented that use the L1-norm and the L∞;-norm of the proposed error function as respective criteria to solve the Squared-Magnitude matching problem. Finally, the reduced model is obtained by applying the factorization technique. Since the poles of the obtained Squared-Magnitude function are prevented from occurring on the JΩ axis (continuous-time case) or unit circle (discrete-time case) by constraint, this approach ensures the stability of the reduced model. Some examples illustrate its applicability.