F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations ", IEEE Signal Processing Magazine, April 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....observed. Processes whose spectra changes with time, are known as nonstationary processes [10] Many (linear and quadratic) techniques have been developed for nonstationary signal processing, but of special importance for us are two linear techniques: 1) the Short Term Fourier Transform, or STFT [11], which is a natural extension of the Fourier transform that Wide sense stationary (WSS) usually requires that the mean and autocorrelation (and in the case of multiple streams, cross correlation) functions of the process are constant with respect to the the time and duration of observation. 8 ....

HLAWATSCH, F., AND BOUDREAUX-BARTELS, G. F. Linear and quadratic time-frequency signal representations. IEEE Signal Processing Magazine 9, 4 (1992), 21--67.

....the stationary spectrum given by the FFT) may not be relevant. TFRs are particularly suited to the analysis of multicomponent chirp signals with time varying amplitude for two reasons. Firstly, TFRs are nonparametric, which implies that no amplitude model need be defined. Secondly, Cohen s class [3, 4] TFRs are adapted to chirp signals; the Wigher Ville distribution [10] from which every TFR in Cohen s class is Emitting line Recording line Sound source (DAT, sound card, oscillator, etc. Amplifier Sound card I Microphone Fig. 3. Recording procedure: First, the test signal is recorded ....

....fault detection. 2.1 Cohen s Class TFRs Recent advances in TF classification detection theory [7 9] have led to increased analysis efficiency. The underlying principle consists of a TFR comparison using a TF distance measure. Cohen s class TFRs, denoted x(t, f) in the following, are defined as [3, 4]: Fig. 4. Spectrogram of the preprocessed response of a NEXO PS15 loudspeaker emitting the multicom ponent chirp test signal. where t denotes the time, f the frequency, b the TFR kernel and Wx(t, f) the Wignet Ville distribution of x: T T Wx(t, f) x(t )x (t ) e j2f dr (4) where ....

F. Hlawatsch and G.F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations," IEEE Signal Processing Magazine, pp. 21 - 67, April 1992.

....results. 1. INTRODUCTION Time Frequency Representations (TFRs) are powerful tools for non stationary signals analysis. Many works concern the improvement of their readability (i.e. concentration both in time and frequency or cross terms suppression) Remaining in the Cohen s group of TFRs [1], the design of optimal signal dependant kernels provides really exciting results [2] 3] This paper deals with the use of TFRs in classification problems, the goal being again to propose a method for the optimization of kernels. In this case, the aim is no longer the readability of TFRs, but ....

F. Hlawatsch and G.F. Boudreaux-Bartels. Linear and quadratic time-frequency signal representations. IEEE SP Magazine, pages 21--67, Apr. 1992.

....observed. Processes whose spectra changes with time, are known as nonstationary processes [10] Many (linear and quadratic) techniques have been developed for nonstationary signal processing, but of special importance for us are two linear techniques: 1) the Short Term Fourier Transform, or STFT [11], which is a natural extension of the Fourier transform that employs shifting temporal windows to divide a nonstationary signal into components over which stationarity can be assumed, and (2) the Wavelet Transform [21] which is more complex than the STFT, but o ers better timefrequency resolution ....

Hlawatsch, F., and Boudreaux-Bartels, G. F. Linear and quadratic time-frequency signal representations. IEEE Signal Processing Magazine 9, 4 (1992), 21-67.

....be done without loss of generality ; it finally leads to: R s (#) I n involving that R y = AA . 3. BILINEAR QUADRATIC TIME FREQUENCY REPRESENTATIONS 3.1. Some recalls 3.1.1. Bilinear and Quadratic TFR A Quadratic Time Frequency Representation (Q TFR) associated to a signal x i (t) is [5] the restriction to x i (t) x j (t) of a bilinear transform applied to a couple (x i , x j ) x i Q TFR D x i = D x i x i such as (x i , x j ) B TFR D x i x j (4) D x i x j (t, #; R) x i (#)x # j (# # )R(#, # # ; t, #) kernel d#d# # . 5) To simplify, we will omit the ....

....Table 2) Finally, it is possible to give some exemples of representations belonging to the Cohen s class: Spectrogram (Sp) Pseudo WignerVille (PWV) Smoothed Pseudo Wigner Ville (SPWV) etc. to the Affine Class: Scalogramme (Sc) and to both classes: Wigner Ville (WV) Cho Williams (CW) see [5] for more details about these representations) Table 1: A summary of Affine and Cohen s class properties definitions Cohen class condition of definition: y(t) x(t #)e 2i##t # y (t, #) # x (t #, # #) Affine class condition of definition: y(t) a x(a(t ....

F. Hlawatsch, G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations ", IEEE Signal Processing Magazine, pp. 21-67, April 1992.

....time frequency windows . 2. There must exist some time frequency windows where only one source is present . Many powerful time frequency methods have been developed during the last fifty years with different application fields. One can find most of them with detailed references in [8] [9], 10] 11] To avoid the interference areas present in the and higher order existing methods, the most relevant starting point to solve our problem is to use the simple short time Fourier transform of the observations as defined in [10] We first Due to statistical fluctuations, even ....

F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations," IEEE Signal Processing Magazine, vol. 9, pp. 21--67, April 1992.

....presence of interference terms. These terms render the WD of multicomponent signals extremely di#cult to interpret. Several methods, developed to reduce noise and cross components at the expense of reduced time frequency energy concentration, employ smoothing kernels or windowing techniques [3,22,24,25]. Unfortunately, the specific choice of kernel dramatically a#ects the appearance and quality of the resulting time frequency representation. Consequently, adaptive representations [1,15,25] often exhibit performance far surpassing that of fixedkernel representations. However, such methods are ....

....and #(t,#) is the 2 D Fourier transform of #(#,#) Di#erent kernels produce di#erent distributions obeying di#erent properties. For example, #(#,#) 1, e#######,e ## ## and w(#) ### sin(###) ### correspond to the Wigner, Page, Choi Williams and Conekernel distributions, respectively [22]. The spectrogram, the squared magnitude of the short time Fourier transform, is also a member of Cohen s class, since it can be obtained as a 2 D convolution of the WDs of the signal and the window. The interference terms associated with the WD are highly oscillatory, whereas the auto terms are ....

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F. Hlawatsch, G.F. Boudreaux-Bartels, Linear and quadratic time---frequency signal representations, IEEE SP Mag. (April 1992) 21---67.

....of interference terms. These terms render the WD of multicomponent signals extremely di#cult or impossible to interpret. Several methods, developed to reduce noise and cross components at the expense of reduced time frequency energy concentration, employ smoothing kernels or windowing techniques [15, 78, 79, 73]. Unfortunately, the specific choice of kernel dramatically a#ects the appearance and quality of the resulting time frequency representation. Consequently, adaptive representations [79, 4, 50] often exhibit performance far surpassing that of fixedkernel representations. However, such methods are ....

....#) is the 2 D Fourier transform of #(#, # ) Di#erent kernels produce di#erent distributions obeying di#erent properties. For example, #(#, #) 1, e j# # 2 , e # # and w(#) # sin(###) ### correspond to the Wigner, Page, Choi Williams and Cone kernel distributions, respectively [73]. The spectrogram, the squared magnitude of the short time Fourier transform, is also a member of Cohen s class, since it can be obtained as a 2 D convolution of the WD s of the signal and the window. The interference terms associated with the WD are highly oscillatory, whereas the auto terms are ....

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations", IEEE SP Magazine, Apr. 1992, pp. 21--67.

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F. Hlawatsch and G. F. Boudreaux-Bartels, \Linear and quadratic time-frequency signal representations," IEEE Signal Processing Magazine, vol. 9, pp. 21-67, April 1992.

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations," IEEE Signal Processing Magazine, vol. 9, pp. 21--67, April 1992.

....an LTV bandpass lter with time varying center frequency and gain. The TF weight function M(n; discretized with K = 64 frequency bins) is shown in Fig. 4.5(a) The input signal x[n] of length 2048 samples consists of three linear chirp components. A smoothed pseudo Wigner distribution (SPWD) [45 47] and the real part of x[n] are shown in Fig. 4.5(b) The output signals of H Z and e HHW are shown in Fig. 4.5(c) d) It is seen that both lters succeed in implementing the desired TF weighting as speci ed by M(n; they extract and amplify the central part of the rst chirp component, ....

....lter; e) output signal of approximate halfband Weyl lter. bins; it was obtained by thresholding an SPWD of x[n] i.e. all SPWD values above threshold were set equal to 1 in M [n; k] It is seen from Fig. 4. 8(c) that M [n; k] contains oscillatory components resulting from SPWD cross terms [45 47] above threshold. These components cause both H Z and e HHW to be overspread , i.e. to introduce undesired TF shifts. Indeed, both output signals (see Fig. 4.8(d) e) contain one or more parasitic components in addition to the desired component. These parasitic components are not due to the ....

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F. Hlawatsch and G. F. Boudreaux-Bartels, \Linear and quadratic time-frequency signal representations, " IEEE Signal Processing Magazine, vol. 9, pp. 21-67, April 1992.

....space depends on the signals to be classified. A variety of approaches have been previously proposed such as a wavelet packet based algo rithm [3] selection of the best basis) and methods based on time frequency representations (TFRs) 4 7] selection of the best TFR within Cohen s class [8]) However, these techniques still suffer from certain restrictions concerning the optimization employed. In this letter, we propose a TFR based approach that uses an improved optimization procedure. The improvement is due to the fact that (i) the distance measure is optimized (in addition to the ....

....of ni signals x (t) k = 1, hi. A. Decision Rule The proposed TF classifier uses the following decision rule: x is assigned to w with = argmin d(2,i ) 1) i=1, N liere, d( is a dissimilarity or distance measure (see Sec tion II B) t, f) is a real valued TFR from Cohen s class [8, 12] (see Section II C) and i(t, f) is a representative TFR characterizing the class wi. Here, we define i(t, f) to be the average of the TFRs of the learning signals x i(t,f) a 1 (t,f) 2) ni k 1 Several TF classifiers previously proposed use the general decision rule (1) 4 6] or a similar ....

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F. Hlawatsch and G.F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations", IEEE SP Magazine, pp. 21-67, April 1992.

.... a two dimensional (2 D) function of time and frequency, Tx(t,f) As a result, QTFRs are potentially capable of displaying the temporal localization of the signal s spectral compo nents [2 6] QTFRs have been used successfully for the analysis and synthesis of nonstationary or transient signals [4]. They are found in applications such as speech processing, signal detection and parameter estimation, the analysis of acoustical and biological signals, and the analysis of linear systems. Some well known QTFRs include the Wigner distribution [2,7,8] the smoothed pseudo Wigner distribution ....

.... the smoothed pseudo Wigner distribution [3 5,8] the Choi Williams (exponential) distribution [3 5,9 11] the generalized exponential distribution [12] the spectrogram (squared magnitude of the short time Fourier transform) 13 15] the scalogram (squared magnitude of the wavelet transform) [4,16,17], the Altes Marinovich Q distribution [18,19] and the Bertrand PK distributions [20 22] Since no one QTFR exists that can be used effectively in all possible applications, different QTFRs are best suited for analyzing signals with different types of properties. Thus, the choice of a QTFR ....

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Hlawatsch, F., and Boudreaux-Bartels, G. F. Linear and quadratic time-frequency signal representations, IEEE Signal Process. Mag. 9 (1992), 217.

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations ", IEEE Signal Processing Magazine, April 1992.

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations", IEEE Signal Processing Magazine, April 1992.

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and Quadratic Time-Frequency Signal Representations, " IEEE SP Magazine, pp. 21--67, Apr. 1992.

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations," IEEE Signal Processing Magazine, vol. 9, pp. 21--67, April 1992.

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations," IEEE SP Magazine, vol. 9, pp. 21--67, April 1992.

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations," IEEE Signal Processing Magazine, vol. 9, pp. 21--67, April 1992.

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and Quadratic TimeFrequency Signal Representations," IEEE Signal Processing Mag., pp 2167, April 1992.

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time--frequency signal representations," IEEE Signal Processing Magazine, vol. 9, pp. 21--67, Apr. 1992.

No context found.

F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations", IEEE Signal Processing Magazine, vol. 9, pp. 21--67, April 1992.

No context found.

F. Hlawatsch and G. F. Boudreaux-Bartels. Linear and quadratic time-frequency signal representations. IEEE SP Magazine, pages 21--67, April 1992.

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations," IEEE Signal Proc. Magazine, pp. 21--67, 1992.

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F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations," IEEE Signal Processing Magazine, April 1992.

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